Vertically Opposite Angles

Q.

In the figure below, OP, OQ, OR and OS are four rays. Then, find $\frac{(\angle POQ+\angle QOR+\angle SOR+\angle POS)}{3}$.

1. ${60}^{\circ }$
2. ${120}^{\circ }$
3. ${90}^{\circ }$
4. ${30}^{\circ }$

Q.

In the figure below, lines AB and CD intersect each other at point O. The angle pairs $(\angle AOD$, $\angle COB)$ and $(\angle AOC$, $\angle BOD)$ are called ___.

1. vertically opposite angles
2. opposite interior angles
3. corresponding angles
4. adjacent pair angles

Q.

In the figure below, lines AB and CD intersect at O. If $\angle$AOC + $\angle$BOE = ${70}^{\circ }$ and $\angle$BOD = ${40}^{\circ }$, find (2 $\angle$BOE).

1. ${50}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. Assertion (A) : If two internal opposite angles of a triangle are equal and external angle is given to be 110°, then each of the equal internal angle is 55°.
Reason (R) : A triangle with one of its angle 90°, is called a right triangle.
[2 marks]

1. Both A and R are true, and R is the correct explanation for A.
2. Both A and R are true, and R is not the correct explanation for A.
3. A is true but R is false.
4. A is false but R is true.

Q. Select the correct option based on the given figure.

1. Insufficient data
2. $\angle$u > $\angle$y
3. $\angle$u = $\angle$y
4. $\angle$u < $\angle$y

Q.

In the figure, given below $\angle$COD = 150${}^{\circ }$. Choose the correct option.

1. BOC = 40

2. AOB = 15

3. None of the above

4. AOB = 150

Q. When two straight lines intersect, which of the following statements is/are true?

1. Adjacent angles are complementary.
2. Adjacent angles are supplementary.
3. Vertically opposite angles are equal.

4. Vertically opposite angles are supplementary.

Q.

In the figure, two lines intersect at O. If x = ${75}^{\circ }$, find $\angle$u + $\angle$y.

1. 

2. 

3. 

4. 

Q.

In the given figure AB and CD are two lines intersecting at O. If $\angle AOC$ and $\angle BOC$ are in ratio 2 : 3, find all angles.

1. ${72}^{\circ },{108}^{\circ },{108}^{\circ },{72}^{\circ }$
2. ${30}^{\circ },{120}^{\circ },{30}^{\circ },{120}^{\circ }$
3. ${50}^{\circ },{120}^{\circ },{50}^{\circ },{120}^{\circ }$
4. ${45}^{\circ },{100}^{\circ },{100}^{\circ },{45}^{\circ }$

Q. In the following figure, $\angle 1=2y+{25}^{\circ },\angle 2=x+{15}^{\circ }$. Find $x$ and $y$, if $2y+{25}^{\circ }=3y$.

1. $x={60}^{\circ },y={20}^{\circ }$
2. $x={65}^{\circ },y={25}^{\circ }$
3. $x={65}^{\circ },y={20}^{\circ }$
4. $x={60}^{\circ },y={25}^{\circ }$