Vertically Opposite Angles

Q.

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.

Q.

Two lines AB and CD intersect at O. If $\angle AOC={50}^{\circ }$, find $\angle AOD,\angle BOD$ and $\angle BOC$.

Q.

Two lines AB and CD intersect at a point O such that $\angle BOC+\angle AOD={280}^{\circ }$, as shown in the figure. Find all the four angles.

Q. If two lines intersect each other, then the vertically opposite angles _______ .

1. are complementary
2. are supplementary
3. form a linear pair
4. are equal

Q.

In the figure if $l||m$ and $\angle 1=(2x+y{)}^{\circ }$ , $\angle 4=(x+2y{)}^{\circ }$ and $\angle 6=(3y+20{)}^{\circ }$. Find $\angle 7$ and $\angle 8$.

Q.

In the figure, lines PQ and RS intersect each other at point O. If $\angle POR:\angle ROQ=5:7$. Find all the angles.

Q.

If two straight line intersect each other in such a way that one of the angles formed measures ${90}^{\circ }$, show that each of the remaining angles measures ${90}^{\circ }$.

Q.

In the figure, what is y in terms of x?

Q.

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

Q.

If two adjacent angles are equal, then each angle measures 90${}^{\circ }$.

1. False

2. True

Q.

Two straight lines AB and CD intersect one another at the point O. If $\angle AOC+\angle COB+\angle BOD={274}^0$, then $\angle AOD$

1. ${86}^0$

2. ${90}^0$
   

3. ${94}^0$

4. ${137}^0$

Q.

The bisector of $\angle B$ and $\angle C$of triangle $ABC$ intersect each other at the point$O$. Prove that$\angle BOC=90°+\frac{1}{2}\angle A.$

Q.

If ray OC stands on line AB such that Angle AOC = Angle BOC then show that
Angle BOC= 90˚

Q.

If two lines intersect and if one pair of vertically opposite angles is formed by acute angles, then the other pair of vertically opposite angles will be formed by obtuse angles.

1. True

2. False

Q.

In the given figure, $\angle OAB={75}^{\circ },\angle OBA={55}^{\circ }$ and $\angle OCD={100}^{\circ }$. Then, $\angle ODC=?$


$\left(a\right){20}^{\circ }$

$\left(b\right){25}^{\circ }$

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

$\left(d\right){35}^{\circ }$

Q.

In the given figure, three lines AB, CD and EF intersect at a point O such that $\angle AOE={35}^{\circ }$ and $\angle BOD={40}^{\circ }$. Find the measure of $\angle AOC,\angle BOF,\angle COF$ and $\angle DOE$.

Q.

In $\Delta ABC,BD\perp AC$ and CE $\perp AB.$ If BD and CE intersect at O , prove that $\angle BOC={180}^{\circ }-\angle A.$

Q. When two lines intersect each other at a point, the angles opposite to each other are called _______.

1. supplementary angles
2. complementary angles
3. adjacent angles
4. vertically opposite angles

Q.

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

Q.

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.

Q. 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 line 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.

Q. Using the information shown in figure, find the measures of $\angle$a, $\angle$b and $\angle$c.

Q.

If two lines intersect each other, then the vertically opposite angles are ……….

1. Supplementary

2. Unequal

3. Equal

4. Complementary

Q.

In the given figure, l || m and a transversal t cut them. If $\angle 1={120}^{\circ }$, find the measure of each of the remaining marked angles.

Q. In the following figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130° find ∠QRS.

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

Q. Question 5
In the given figure, if $PQ\perp PS,PQ||SR,\angle SQR={28}^{\circ }$ and $\angle QRT={65}^{\circ }$, then find the values of x and y.

Q. In the triangle ABC, the bisectors of the exterior angles B and C meet at O. Given angle $BAC={60}^{\circ }$ and angle $ABC={70}^{\circ }$. Find angle BOC.

Q.

In the below figure, ABCDEF is a regular hexagon, and its center is point O. Find the value of x?

1. 80°

2. 60°

3. 40°

4. 30°

Q. 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.