Define the following terms:

(i) Angle

(ii) Interior of an angle

(iii) Obtuse angle

(iv) Reflex angle

(v) Complementary angles

(vi) Supplementary angles

If = 36°27’46’’and =28°43’39’’, find +.

Find the difference between two angles measuring 36° and 24°28’30’’

Find the complement of each of the following angles.

(i) 58°

(ii) 16°

(iii) of a right angle

(iv) 46°30’

(v) 52°43’20’’

(vi) 68°35’45’’

Find the supplement of each of the following angles.

(i) 63°

(ii) 138°

(iii) of a right angle

(iv) 75°36’

(v) 124°20’40’’

(vi) 108°48’32’’

Find the measure of an angle which is

(i) equal to its complement,

(ii) equal to its supplement.

Find the measure of an angle which is 36° more than its complement.

Find the measure of an angle which 25°less than its supplement.

Find the angle which is four times its complement.

Find the angle which is five times its supplement.

Find the angle whose supplement is four times its complement.

Find the angle whose complement is four times its supplement.

Two supplementary angles are in the ratio 3:2 Find the angles.

Two complementary angles are in the ratio 4:5 Find the angles.

Find the measure of an angle, if seven times its complement is 10° less than three times its supplement.

In the adjoining figure, AOB is a straight line. Find the value of x.

In the adjoining figure, AOB is a straight line. Find the value of x. Hence, Find And

In the adjoining figure, AOB is a straight line. Find the value of x. Hence, find,and .

In the adjoining figure, x: y: z =5:4:6. If XOY is a straight line, find the values of x, y and z

In the adjoining figure, what value of x will make AOB, a straight line?

Two lines AB and CD intersect at O. If =50°^, find and .

In the adjoining figure, there coplanar lines AB, CD and EF intersect at a point O, forming angles as shown. Find the values of x, y, z and t.

In the adjoining, there coplanar lines AB, CD and EF intersect at a point O. Find the value of x. Hence, find,and .

Two adjacent angles on a straight line are in the ratio 5:4 Find the measure of each one of these angles.

If two straight lines intersect each other in such a way that one of the angles formed measure 90°, show that each of the remaining angles measures 90°.

Two lines AB and CD intersect at a point O such that + =280°, as shown in the figure. Find all the four angles.

In the given figure, ray OC is the bisector of and OD is the ray opposite to OC. Show that =.

In the given figure, AB is a mirror; PQ is the incident ray and QR, the reflected ray. If =112°, Find .

If two straight lines intersect each other then prove that the ray opposite to the bisector of one of the angles so formed bisects the vertically opposite angle.

Prove that the bisectors of two adjacent supplementary angles include a right angle.

Secondary school Mathematics for class 9

In the adjoining figure, AB ||CD are cut by a transversal t at E and F respectively. If =70°, Find measure of each of the remaining marked angles.

In the adjoining figure, AB ||CD are cut by a transversal t at E and F respectively. If =5:4, Find measure of each of the remaining marked angles.

In the adjoining figure, ABCD is a quadrilateral in which AB||DC and AD||BC. Prove that =.

In each of the figure given below, AB||CD. Find the value of x in each case.

(i)

(ii)

(iii)

In the given figure, AB||CD ||EF. Find the value of x.

In the given figure, AB||CD. Find the value of x.

In the given figure, AB||CD. Prove that -=.

In the given figure, AB||CD and BC||ED. Find the value of x.

In the given figure, AB||CD. Prove that p+q-r=180

In the given figure, AB||PQ. Find the value of x and y.

In the given figure, AB ||CD. Find the value of x.

In the given figure, AB||CD. Find the value of x.

In the given figure, AB||CD. Find the value of x, y and z.

In the given figure, AB||CD. Find the values of x, y and z.

In the given figure, AB||CD and EF||GH. Find the values of x, y, z and t.

For what value of x will the lines I and m be parallel to each other?

(i).

(ii)

If two straight lines are perpendicular to the same line, prove that they are parallel to each other.

The angles of a triangle are in the ratio 2:3:4. Find the angles.

In , if 3= 4=6, calculate, and .

In , if +=108°and+ =130°,Find ,and.

In , if +=125°and+ =113°,Find ,and.

In, if -=42°and-=21°, Find,and.

The sum of two angles of a triangle is 116° and their difference is 24°.Find the measure of each angle of the triangle.

Of the three angles of a triangle are equal and the third angle is greater than each one of them by 18°. Find the angle.

Of the three angles of a triangle, one is twice the smallest and mother one is thrice the smallest. Find the angle.

In a right-angled triangle, one of the acute measures 53°^. Find the measure of each angle of the triangle.

If one angle of a triangle is equal to the sum of the other two, show that the triangle is right angled.

A is right angled at A. If AL BC, prove that =.

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

If each angle of a triangle is greater than the sum of the other two, show that the triangle is obtuse angled.

In the given figure, side BC of ABC is produced to D. If =128° and =43°,Find and .

In the given figure, the side BC of has been produced on both sides-on the left to D and on the right to E. If =106° and =118°^, Find the measure of each angle of the triangle.

Calculate the value of x in each of the following figure.

(i).

(ii)

(iii)

(iv)

(v)

(vi)

Calculate the value of x in the given figure.

In the given figure, AD divides in the ratio 1:3 and AD=DB. Determine the value of.

If the side of a triangle are produced in order, Prove that the sum of the exterior angles so formed is equal to four right angles.

In the adjoining figure, show that +++++=360°

In ABC the angle bisectors of and meet at O. If =70°,Find .

The sides AB and AC of ABC have been produced to D and E respectively. The bisectors of and meet at O. If =40° find .

In the given figure, ABC is a triangle in which::=3:2:1 and AC CD. Find the measure of.

In the given figure, AM BC and AN is the bisector of. Find the measure of.

State ‘True’ or ‘false’:

(i) A triangle can have two right angles.

(ii) A triangle cannot have two obtuse angles.

(iii) A triangle cannot have two acute angles.

(iv) A triangle can have each angle less than 60°.

(v) A triangle can have each angle equal to 60°.

(vi) There cannot be a triangle whose angles measure 10°, 80° and 100°.

If two angles are complements of each other, then each angle is

An angle which measures more than 180° but less than 360°, is called

The complement of 72°40’ is

The supplement of 54°30’ is

The measure of an angle is five times its complement. The angle measures

Two complementary angles are such that twice the measure of the one is equal to three times the measure of the other. The larger of the two measures

Two straight lines AB and CD cut each other at O. If ∠BOD = 63°, then ∠BOD = ?

In the given figure, AOB is a straight line. If ∠AOC + ∠BOD = 95°, then ∠COD = ?

In the given figure, AOB is a straight line. If ∠AOC = 4x° and ∠BOC = 5x°, then ∠AOC = ?

In the given figure, AOB is a straight line. If ∠AOC (3x + 10)° and ∠BOC = (4x – 26)°, then ∠BOC = ?

In the given figure, AOB is a straight line. If ∠AOC = 40°, ∠COD = 4x°, and ∠BOD = 3x°, then ∠COD = ?

In the given figure, AOB is a straight line. If ∠AOC = (3x – 10)°, ∠COD = 50° and ∠BOD = (x + 20)°, then ∠AOC = ?

Which of the following statements is false?

An angle is one – fifth of its supplement. The measure of the angle is

In the adjoining figure, AOB is a straight line. If x : y : z = 4 : 5 : 6, then y = ?

In the given figure, straight lines AB and CD intersect at O. If ∠AOC = ϕ, ∠BOC = θ and θ = 3θ, then θ = ?

In the given figure, straight lines AB and CD intersect at O. If ∠AOC + ∠BOD = 130°, then ∠AOD = ?

In the given figure AB is a mirror, PQ is the incident ray and QR is the reflected ray. If ∠PQR = 108°, then ∠AQP = ?

In the given figure AB || CD. If ∠OAB = 124°, ∠OCD = 136°, then ∠AOC = ?

In the given figure AB || CD and O is a point joined with B and D, as shown in the figure such that ∠ABO = 35 and ∠CDO = 40°. Reflex ∠BOD = ?

In the given figure, AB || CD. If ∠ABO = 130° and ∠OCD = 110°, then ∠BOC = ?

In the given figure, AB || CD. If ∠BAO = 60° and ∠OCD = 110°, then ∠AOC = ?

In the given figure, AB || CD. If ∠AOC = 30° and ∠OAB = 100°, then ∠OCD = ?

In the given figure, AB || CD. If ∠CAB = 80° and ∠EFC = 25°, then ∠CEF = ?

In the given figure, AB || CD. If ∠APQ = 70° and ∠PRD = 120°, then ∠QPR = ?

In the given figure, x = ?

If 3∠A = 4∠B = 6∠C, then A : B : C = ?

In ΔABC, if ∠A + ∠B = 125° and ∠A + ∠C = 113°, then ∠A = ?

In ΔABC, if ∠A – ∠B = 42° and ∠B – ∠C = 21°, then ∠B = ?

In ΔABC, side BC is produced to D. If ∠ABC = 40° and ∠ACD = 120°, then ∠A = ?

Side BC of ΔABC has been produced to D on left hand side and to E on right hand side such that ∠ABD = 125° and ∠ACE = 130°. Then ∠A = ?

In the given figure, ∠BAC = 30°, ∠ABC = 50° and ∠CDE = 40°. Then ∠AED = ?

In the given figure, ∠BAC = 40°, ∠ACB = 90° and ∠BED = 100°. Then ∠BDE = ?

In the given figure, BO and CO are the bisectors of ∠B and ∠C respectively. If ∠A = 50°, then ∠BOC = ?

In the given figure, AB || CD. If ∠EAB = 50° and ∠ECD = 60°, then ∠AEB = ?

In the given figure, ∠OAB = 75°, ∠OBA = 55° and ∠OCD = 100°. Then ∠ODC = ?

In a ΔABC its is given that ∠A : ∠B : ∠C = 3 : 2 : 1 and CD ⊥ AC. Then ∠ECD = ?

In the given figure, AB || CD. If ∠ABO = 45° and ∠COD = 100° then ∠CDO = ?

In the given figure, AB || DC, ∠BAD = 90°, ∠CBD = 28° and ∠BCE = 65°. Then ∠ABD = ?

For what value of x shall we have l || m?

For what value of x shall we have l || m?

In the given figure, sides CB and BA of ΔABC have been produced to D and E respectively such that ∠ABD = 110° and ∠CAE = 135°. Then ∠ACB = ?

In ΔABC, BD ⊥ AC, ∠CAE = 30° and ∠CBD = 40°. Then ∠AEB = ?

In the given figure, AB || CD, CD || EF and y : z = 3 : 7, then x = ?

In the given figure, AB || CD || EF, EA ⊥ AB and BDE is the transversal such that ∠DEF = 55°. Then ∠AEB = ?

In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠ABC = 70° and ∠ACB = 20°, then ∠MAN = ?

An exterior angle of a triangle is 110° and one of its interior opposite angles is 45°, then the other interior opposite angle is

The sides BC, CA and AB of ΔABC have been produced to D, E and F respectively as shown in the figure, forming exterior angles ∠ACD, ∠BAE and ∠CBF. Then, ∠ACD + ∠BAE + ∠CBF = ?

The angles of a triangle are in the ratio 3:5:7. The triangle is

If the vertical angle of a triangle is 130°, then the angle between the bisectors of the base angles of the triangle is

The sides BC, BA and CA of ΔABC have been produced to D, E and F respectively, as shown in the given figure. Then, ∠B = ?

In the adjoining figure, y = ?

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Each question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Match the following columns:

The correct answer is:

A. – …….., B. – ……….,

C. – ………, D. – ……….,

Match the following columns:

The correct answer is:

A. – …….., B. – ……….,

C. – ………, D. – ……….,

The angles of a triangle are in the ratio 3:2:7. Find the measure of each of its angles.

In a ΔABC, if ∠A – ∠B = 40° and ∠B – ∠C = 10°, find the measure of ∠A, ∠B and ∠C.

The side BC of ΔABC has been increased on both sides as shown. If ∠ABD = 105° and ∠ACE = 110°, then find ∠A.

Prove that the bisectors of two adjacent supplementary angles include a right angle.

If one angle of a triangle is equal to the sum of the two other angles, show that the triangle is right – angled.

In the given figure, ACB is a straight line and CD is a line segment such that ∠ACD = (3x – 5)° and ∠BCD = (2x + 10)°. Then, x = ?

In the given figure, AOB is a straight line. If ∠AOC = 40°, ∠COD = 4x° and ∠BOD = 3xׄ°, then x = ?

The supplement of an angle is six times its complement. The measure of this angle is

In the given figure, AB || CD || EF. If ∠ABC = 85°, ∠BCE = x° and ∠CEF = 130°, then x = ?

In the given figure, AB || CD, ∠BAD = 30° and ∠ECD = 50°. Find ∠CED.

In the given figure, BAD || EF, ∠AEF = 55° and ∠ACB = 25°, find ∠ABC.

In the given figure, BE ⊥ AC, ∠DAC = 30° and ∠DBE = 40°. Find ∠ACB and ∠ADB.

In the given figure, AB || CD and EF is a transversal, cutting them at G and H respectively. If ∠EGB = 35° and QP ⊥ EF, find the measure of ∠PQH.

In the given figure, AB || CD and EF ⊥ AB. If EG is the transversal such that ∠GED = 130°, find ∠EGF.

Match the following columns:

The correct answer is:

A. – …….., B. – ……….,

C. – ………, D. – ……….,

In the given figure, lines AB and CD intersect at O such that ∠AOD + ∠BOD + ∠BOC = 300°. Find ∠AOD.

In the given figure AB || CD, ∠APQ = 50° and ∠PRD = 120°. Find ∠QPR.

In the given figure, BE is the bisector of ∠B and CE is the bisector of ∠ACD.

Prove that

In ΔABC, sides AB and AC are produced to D and E respectively. BO and CO are the bisectors of ∠CBD and ∠BCE respectively. Then, prove that

Of the three angles of a triangle, one is twice the smallest and another one is thrice the smallest. Find the angles.

In ΔABC, ∠B = 90° and BD ⊥ AC. Prove that ∠ABD = ∠ACB.