In a Δ ABC, if ∠A = 55°, ∠B = 40°, find ∠C

If the angles of a triangle are in the ratio 1 : 2 : 3, determine three angles.

The angles of a triangle are (x-40)°, (x-20)° and. Find the value of x.

The angles of a triangle are arranged ascending order of magnitude. If the difference between two consecutive angles is 10°, find the three angles.

Two angles of a triangle are equal and the third angle is greater than each of those angles by 30°. Determine all the angles of the triangle.

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

ABC is a triangle in which ∠A = 72°, the internal bisectors of angles B and C meet in O. Find the magnitude of ∠BOC.

The bisectors of base angles of a triangle cannot enclose a right angle in any case.

If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.

In a Δ ABC, ∠ABC =∠ACB and the bisectors of ∠ABC and ∠ACB intersect at O such that ∠BOC = 120°. Shoe that ∠A =∠B =∠C = 60°.

Can a triangle have:

(i) Two right angles?

(ii) Two obtuse angles?

(iii) Two acute angles?

(iv) All angles more than 60°?

(v) All angles less than 60°?

(vi) All angles equal to 60°?

Justify your answer in each case.

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

The exterior angles, obtained on producing the base of a triangle both ways are 104° and 136°. Find all the angles of the triangle.

In a ΔABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠B and ∠C meet at Q. Prove that ∠BPC + ∠BQC = 180°.

In Fig. 9.30, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.

Compute the value of x in each of the following figures:

(i)

(ii)

(iii)

(iv)

In Fig. 9.35, AB divides ∠DAC in the ratio 1: 3 and AB =DB. Determine the value of x.

ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = ∠A.

In Fig. 9.36, AC ⊥ CE and ∠A : ∠B :∠C = 3:2:1, find the value of ∠ECD.

In Fig. 9.37, AM ⊥ BC and AN is the bisector of ∠A. If ∠B =65° and ∠C =33°, find ∠MAN.

In a Δ ABC, AD bisects ∠A and ∠C >∠B. Prove that ∠ADB >∠ADC.

In Δ ABC, BD ⊥ AC and CE ⊥ AB. If BD and CE intersect at O, prove that ∠BOC = 180° - A.

In Fig. 9.38, AE bisects ∠CAD and ∠B =∠C. Prove that AE||BC.

In Fig. 9.39, AB||DE. Find ∠ACD.

Which of the following statements are true (T) and which are false (F).

(i) Sum of the three angles of a triangle is 180°.

(ii) A triangle can have two right angles.

(iii) All the angles of a triangle can be less than 60°.

(iv) All the angles of a triangle can be greater than 60°.

(v) All the angles of a triangle can be equal to 60°.

(vi) A triangle can have two obtuse angles.

(vii) A triangle can have at most one obtuse angles.

(viii) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

(ix) An exterior angle of a triangle is led than either of its interior opposite angles.

(x) An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

(xi) An exterior angle of a triangle is greater than the opposite interior angles.

Fill in the blanks to make the following statements true :

(i) Sum of the angles of a triangle is ……

(ii) An exterior angle of a triangle is equal to the two …… opposite angles.

(iii) An exterior angle of a triangle is always …..than either of the interior opposite angles.

(iv) A triangle cannot have more than ….right angles.

(v) A triangles cannot have more than ….. obtuse angles.

Define a triangle.

Write the sum of the angles of an obtuse triangle.

In Δ ABC, if ∠B = 60°, ∠C = 80° and the bisectors of angles ∠ABC and ∠ACB meet at a point O, then find the measure of ∠BOC.

If the angles of a triangle are in the ratio 2: 1: 3, then find the measure of smallest angle.

If the angles A, B and C of Δ ABC satisfy the relation B – A = C – B, then find the measure of ∠B.

In Δ ABC, if bisectors of ∠ABC and ∠ACB intersect at O angle of 120°, then find the measure of ∠A.

State exterior angle theorem.

If the side BC of Δ ABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.

In a triangle ABC, if AB = AC and AB is produced to D such that BD = BC, find ∠ACD: ∠ADC.

The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.

In Fig. 9.40, if AB||CD, EF||BC, ∠BAC = 65° and ∠DHF = 35°, find ∠AGH.

In Fig. 9.41, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find a and y.

In Fig. 9.42, side BC of Δ ABC is produced to point D such that bisectors of ∠ABC and ∠ACD meet at a point E. If ∠BAC = 68°, find ∠BEC.

If all the three angles of a triangle are equal, then each one of them is equal to

If two acute angles of a right triangle are equal, then each is equal to

An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal, each of these angles is equal to

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = ∠A, then ∠A is equal to

In Δ ABC ∠B= ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX =70°, then ∠ACB =

In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure of the other interior angle is

If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is

In Δ ABC, if ∠A = 100° AD bisects ∠A and AD⊥BC. Then, ∠B =

An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are

In a Δ ABC, If ∠A = 60°, ∠B =80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC=

If the bisectors of the acute angles of a right triangle meet at O, then the angle at O between the two bisectors is

Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB =55°, then ∠BOD =

The bisectors of exterior angles at B and C of Δ ABC meet at O, if ∠A= x°, then ∠BOC =

In Δ ABC, ∠A=50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACD meet at E, then ∠E =

The side BC of Δ ABC is produced to a point D. The bisector of ∠A meets side BC in L, If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC =

In Fig. 9.43, if EC||AB, ∠ECD =70° and ∠BDO =20° , then ∠OBD is

In Fig. 9.44, x + y =

If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?

In Fig. 9.45, if AB ⊥ BC, then x =

In Fig. 9.46, what is z in terms of x and y?

In Fig. 9.47, for which value of x is l₁ || l₂?

In Fig. 9.48, what is y in terms of x?

In Fig. 9.49, if l₁ || l₂, the value of x is

In Fig. 9.50, what is value of x?

In Δ RST (See Fig. 9.51), what is value of x ?

In Fig. 9.52, the value of x is

In Fig. 9.53, if BP||CQ and AC=BC, then the measure of x is

In Fig. 9.54, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠APR=25°, ∠RQC=30° and ∠CQF= 65°, then

The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC=