Write the complement of each of the following angles:

(i) 20° (ii) 35° (iii) 90°

(iv) 77° (v) 30°

Write the supplement of each of the following angles:

(i) 54° (ii) 132° (iii) 138°

If an angle is 28° less than its complement, find its measure.

If an angle is 30° more than one half of its complement, find the measure of the angle.

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

Two supplementary angles differ by 48°. Find the angles.

An angle is equal to 8 times its complement. Determine its measure.

If the angles (2x-10)° and (x-5)° are complementary angles, find x.

If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle.

If an angle differs from its complement by 10°, find the angle.

If the supplement of an angle is three times its complement, find the angle.

If the supplement of an angle is two-third of itself. Determine the angle and its supplement.

An angle is 14° more than its complementary angle. What is its measure?

The measure of an angle is twice the measure of its supplementary angle. Find its measure.

In Fig. 8.31, OA and OB are opposite rays:

(i) If x = 25°, what is the value of y?

(ii) If y = 35°, what is the value of x?

In Fig. 8.32, write all pairs of adjacent angles and all the linear pairs.

In Fig. 8.33, find x. Further find ∠BOC, ∠COD and ∠AOD.

In Fig. 8.34, rays OA, OB, OC, OD and OE have the common end point O. Show that ∠AOB +∠BOC +∠COD +∠DOE + ∠EOA = 360°.

In Fig. 8.35, ∠AOC and ∠BOC form a linear pair. If a -2b = 30°, find a and b.

How many pairs of adjacent angles are formed when two lines intersect in a point?

How many pairs of adjacent angles, in all, can you name in Fig. 8.36.

In Fig. 8.37, determine the value of x.

In Fig. 8.38, AOC is a line, find x.

In Fig. 8.39, POS is a line, find x.

In Fig. 8.40, ∠ACB is a line such that ∠DCA = 5x and ∠DCB = 4x. Find the value of x.

Given ∠POR = 3x and ∠QOR = 2x+10, find the value of x for which POQ will be a line.

In Fig. 8.42, a is greater than b by one third of a right angle. Find the values of a and b.

What value of y would make AOB a line in Fig. 8.43, if ∠AOC= 4y and ∠BOC =(6y+30)

In Fig. 8.44, ∠AOF and ∠FOG form a linear pair.

∠EOB = ∠FOC = 90° and ∠DOC = ∠FOG = ∠AOB = 30°

(i) Find the measures of ∠FOE, ∠COB and ∠DOE.

(ii) Name all the right angles.

(iii) Name three pairs of adjacent complementary angles.

(iv) Name three pairs of adjacent supplementary angles.

(v) Name three pairs of adjacent angles.

In Fig. 8.45, OP, OQ, OR and OS are four rays, prove that:

∠POQ + ∠QOR + ∠SOR + ∠POS = 360°

In Fig. 8.46, ray OS stand on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠ respectively. If ∠POS = x, find ∠ROT.

In Fig. 8.47, lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles.

In Fig. 8.48, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = (∠QOS –∠POS.)

In Fig 8.56, lines l₁ and l₂ intersect at O, forming angles as shown in the figure. If x = 45, find the values of y, z and u.

In Fig. 8.57, three coplanar lines intersect at a point O, forming angles as shown in the figure, Find the values of x, y, z and u.

In Fig. 8.58, find the values of x, y and z.

In Fig. 8.59, find the value of x.

Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.

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

If one of the four angles formed by two intersecting lines is a right angle, then show that each of the four angles is a right angle.

In Fig. 8.60, ray AB and CD intersect at O.

(i) Determine y when x = 60°

(ii) Determine x when y = 40^o

In Fig. 8.61, lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠COF, ∠DOE and ∠BOF.

AB, CD and EF are three concurrent lines passing through the point O such that OF bisects ∠BOD. If ∠BOF = 35°, find ∠BOC and ∠AOD.

In Fig. 8.62, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40° find ∠BOE and reflex ∠COE.

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

(i) Angles forming a linear pair are supplementary.

(ii) If two adjacent angles are equal, then each angle measures 90°.

(iii) Angles forming a linear pair can both be acute angles.

(iv) If angles forming a linear pair are equal, then each of these angles is of measure 90°.

Fill in the blanks so as to make the following statements true:

(i) If one angle of a linear pair is acute, then its other angle will be ………..

(ii) A ray stands on a line, then the sum of the two adjacent angles so formed is …………

(iii) If the sum of two adjacent angles is 180°, then the ………….arms of the two angles are opposites rays.

In Fig 8.105, AB, CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all angles from 1 to 8.

In Fig 8.106, l, m and n are parallel lines intersected by transversal p at X, Y and and Z respectively. Find ∠1, ∠2 and∠3.

In Fig 8.107, AB ||CD ||EF and GH ||KL. Find ∠HKL.

In Fig 8.108, show that AB|| EF.

In Fig 8.109, if AB ||CD and CD||EF, find ∠ACE.

In Fig 8.110, PQ||AB and PR||BC. If ∠QPR = 102°, determine ∠ABC. Give reasons.

In Fig 8.111, state which lines are parallel and why?

In Fig 8.112, if l||m, n||p and ∠1 =85°, find ∠2.

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

Prove that the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

In Fig 8.113, lines AB and CD are parallel and P is any point as shown in the figure. Show that ∠ABP +∠CDP = ∠DPB.

In Fig 8.114, AB||CD and P is any point shown in the figure. Prove that:

∠ABP + ∠BPD + ∠CDP = 360°

Two unequal angles of a parallelogram are in the ratio 2 : 3. Find all its angles in degrees.

If each of the two lines is perpendicular to the same line, what kind of lines are they to each other?

In Fig 8.115, ∠1=60° and ∠2= if a right angle. Prove that l||m.

In Fig 8.116, if l||m||n and ∠1 = 60°, find ∠2

Prove that the straight lines perpendicular to the same straight line are parallel to one another.

The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60° find the other angles.

Two lines AB and CD intersect at O. If ∠AOC +∠COB+∠BOD = 270°, find the measures of ∠AOC, ∠COB, ∠BOD and ∠DOA.

In Fig 8.117, p is a transversal to lines m and n, ∠2 = 120° and ∠5 = 60°. Prove that m||n.

In Fig 8.118, transversal l intersects two lines m and n, ∠4= 110° and ∠7 = 65°. Is m||n?

Which pair of lines in fig 8.119 are parallel? Given reasons

If, l, m, n are three lines such that l||m and n⊥ l, prove that n⊥ m.

In Fig 8.120, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC = ∠DEF.

In Fig 8.121, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC + ∠DEF = 180°

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

(i) If two lines are intersected by a transversal, then corresponding angles are equal.

(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

(iii) Two lines perpendicular to the same line are perpendicular to each other.

(iv) Two lines parallel to the same line are parallel to each other.

(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Fill in the blanks in each of the following to make the statement true:

(i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are …..

(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ……….

(iii) Two lines perpendicular to the same line are …….. to each other.

(iv) Two lines parallel to the same line are ….. to each other.

(v) If a transversal intersects a pair of lines in such away that a pair of alternate angles are equal, then the lines are …………

(vi) If a transversal intersects a pair of lines in such away that the sum of interior angles on the same side of transversal is 180°, then the lines are ……

Define complementary angles.

Define supplementary angles.

Define adjacent angles.

The complement of an acute angle is ……….

The supplement of an acute angle is ……….

The supplement of a right angle is ……….

Write the complement of an angle of measure x°.

Write the supplement of an angle of measure 2y°.

If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes.

An angle is equal to its supplement. Determine its measure.

An angle is equal to five times its complement. Determine its measure.

How many pairs of adjacent angles are formed when two lines intersect in a point?

One angle is equal to three times its supplement. The measure of the angle is

Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is

Two straight lines AB and CD intersect one another at the point O. If ∠AOC+∠COB+∠BOD = 274°, then ∠AOD =

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

Consider the following statements:

When two straight lines intersect:

(i) 0Adjacent angles are complementary

(ii) Adjacent angles are supplementary.

(iii) Opposite angles are equal.

(iv) Opposite angles are supplementary.

Of these statements

Given ∠POR = 3x and ∠QOR =2x+10°. If ∠POQ is a straight line, then the value of x is

In Fig. 8.122, AOB is a straight line. If ∠AOC +∠BOD = 85°, then ∠COD =

In Fig. 8.123, the value of y is

In Fig. 8.124, if = 5 and = 4, then the value of x is

In Fig. 8.125, the value of x is

In Fig. 8.126, which of the following statements must be true?

(i) a + b = d + c

(ii) a + c + e =180°

(iii) b + f = c + e

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then the measure of the larger angle is

In Fig. 8.127, AB||CD||EF and GH||KL. The measure of ∠HKL is

In Fig. 8.128, if AB||CD, then the value of x is

AB and CD are two parallel lines. PQ cuts AB and CD at E and F respectively. EL is the bisector of ∠FEB. If ∠LEB =35°, then ∠CFQ will be

Two lines AB and CD intersect at O. If ∠AOC +∠COB +∠BOD = 270°, then ∠AOC =

In Fig. 8.129, PQ++RS, ∠AEF =95°, ∠BHS =110° and ∠ABC =x°. Then the value of x is,

In Fig. 8.130, if l₁||l₂, what is the value of x?

In Fig. 8.131, if l₁ || l₂, what is x + y in terms of w and z?

In Fig. 8.132, if l₁ || l₂, what is the value of y?

In Fig. 8.133, if l₁ || l₂ and l₃ || l₄, what is y in the terms of x?

In Fig. 8.134, if l || m, what is the value of x?

In Fig. 8.135, if line segment AB is parallel to the line segment CD, what is the value of y?

In Fig. 8.136, if CP || DQ, then the measure of x is

In Fig. 8.137, if AB|| HF and DE||FG, then the measure of ∠FDE is

In Fig. 8.138, if lines l and m are parallel, then x =

In Fig. 8.139, if AB||CD, then x =

In Fig. 8.140, if lines l and m are parallel lines, then x =

In Fig. 8.141, if l || m, then x =

In Fig. 8.142, if lines l and m are parallel, then the value of x is