Linear Pair

Q.

In the adjoining figure, AOB is a straight line. Find the value of x. Hence, find $\angle AOC,\angle COD$ and $\angle BOD$.

Q.

In the figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that $\angle ROS=\frac{1}{2}(\angle QOS-\angle POS)$.

Q.

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

Q.

In the figure, lines $AB$ and $CD$ intersect at $O$. If $\angle AOC+\angle BOE={70}^{\circ }$ and $\angle BOD={40}^{\circ }$, find $\angle BOE$ and reflex $\angle COE$.

Q.

In the given figure, $AOB$ is a straight line. If $\angle AOC=(3x+10{)}^{\circ }$ and $\angle BOC=(4x-26{)}^{\circ }$, then $\angle BOC=?$

(a) ${96}^{\circ }$

(b) ${86}^{\circ }$

(c) ${76}^{\circ }$

(d) ${106}^{\circ }$.

Q.

Given $\angle POR=3x$ and $\angle QOR=2x+{10}^{\circ }$, find the value of x for which POQ will be a line.

Q.

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

Q.

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

Q.

In the given figure, AOB is a straight line. If $\angle AOC=(3x-10{)}^{\circ }$, \angle COD = 50^{\circ}\) and $\angle BOD=(x+20{)}^{\circ }$ then $\angle AOC=?$

(a) ${40}^{\circ }$

(b) ${60}^{\circ }$

(c) ${80}^{\circ }$

(d) ${50}^{\circ }$

Q.

In the given figure, AOB is a straight line. If $\angle AOC=4x^{\circ }$ and $\angle BOC=5x^{\circ }$ then $\angle AOC=?$

(a) ${40}^{\circ }$

(b) ${60}^{\circ }$

(c) ${80}^{\circ }$

(d) ${100}^{\circ }$

Q.

In the figure, find the values x, y and z.

Q.

In the figure, $\angle AOC$ and form a linear pair. If $a-2b={30}^{\circ }$, find $a$ and $b$.

Q.

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

Q.

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

Q.

Two lines AB and CD intersect at O. If $\angle AOC+\angle COB+\angle BOD={270}^0$, then $\angle AOC$ =

Q.

In the adjoining figure, what is the value of y?
(a) 36
(b) 54
(c) 63
(d) 72

Q. In the figure, the value of x is ________.

1. ${20}^{\circ }$
2. ${10}^{\circ }$
3. ${15}^{\circ }$
4. ${25}^{\circ }$

Q.

A pair of angles is called linear pair if sum of two adjacent angles is:

1. 90^o

2. 270^o

3. 360^o

4. 180^o

Q.

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

(a) ${60}^{\circ }$

(b) ${80}^{\circ }$

(c) ${48}^{\circ }$

(d) ${72}^{\circ }$

Q.

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

Q.

Two straight lines AB and CD cut each other at O. If $\angle BOD={63}^0$, then $\angle BOC$

1. ${63}^0$

2. ${117}^0$
   

3. ${17}^0$

4. ${153}^0$

Q.

If angles forming a linear pair are equal, then each of these angles is of measure 90${}^{\circ }$.

1. False

2. True

Q.

In the figure, determine the value of x.

Q.

In the given figure; AB is a mirror, PQ is the incident ray and QR is the reflected ray. If $\angle PQR={108}^{\circ }$ then $\angle AQP=?$

$\left(a\right){72}^{\circ }$

$\left(b\right){18}^{\circ }$

$\left(c\right){36}^{\circ }$

$\left(d\right){54}^{\circ }$

Q.

In the given figure, AOB is a straight line. The value of x is

(a) 12

(b) 15

(c) 20

(d) 25

Q.

In the given figure, straight lines AB and CD intrsect at O. If $\angle AOC=\varphi ,\angle BOC=\theta$ and $\theta =3\varphi$, then $\varphi =?$

$\left(a\right){30}^{\circ }$

$\left(b\right){40}^{\circ }$

$\left(c\right){45}^{\circ }$

$\left(d\right){60}^{\circ }$

Q. Sum of interior angle and exterior angle at a vertex is:

1. ${90}^{\circ }$.
2. ${270}^{\circ }$.
3. ${180}^{\circ }$.
4. ${360}^{\circ }$.

Q.

In the figure, OP, OQ, OR and OS are four rays.
Prove that: $\angle POQ+\angle QOR+\angle SOR+\angle POS={360}^{\circ }$

Q.

In the figure, rays OA, OB, OC, OD and OE have the common end point O. Show that $\angle AOB+\angle BOC+\angle COD+\angle DOE+\angle EOA={360}^{\circ }$.

Q.

In the given figure, lines XY and MN intersect at O. If ∠POY = and a:b = 2 : 3, find c.