Vertically Opposite Angles

Q. Define linear pair of angles?

Q.

In the figure, two straight lines PQ and RS intersect each other at O. If $\angle POT={75}^{\circ }$, find the values of a, b and c. [4 MARKS]

Q.

Two angles forming a linear pair are always _____.

Q.

Sum of vertically opposite angles is always 180°. State true or false.

1. True
2. False

Q.

A horizontal line and a vertical line always intersect at right angles.

1. True

2. False

Q.

Question 91

Amisha makes a star with the help of line segments a, b, c, d, e and f in which $a||d,$ $b||e$ and $c||f.$ Chhaya marks an angle as ${120}^{\circ }$ as shown in the given figure and Amisha to find to $\angle x,\angle y$and $\angle z.$ Help Amisha in finding the angles.

Q.

If two adjacent angles are supplementary, they form a ___________.

Q.

Q.

Question 14 (i)
In the adjoining figure, name the following pairs of angles:
Obtuse vertically opposite angles.

Q. If two lines intersect at a point, then the vertically opposite angles are always equal.

1. True
2. False

Q. Find the values of the angles x, y and z in the following figure.

1. $x={55}^{\circ },y={135}^{\circ }andz={135}^{\circ }$
2. $x={55}^{\circ },y={125}^{\circ }andz={125}^{\circ }$
3. $x={45}^{\circ },y={225}^{\circ }andz={25}^{\circ }$
4. $x={35}^{\circ },y={145}^{\circ }andz={125}^{\circ }$

Q.

Find the value of the unknowns $x$ and $y$ in the following diagrams:

Q. In the given figure, lines PQ, RS and TV intersect at O. If x : y : z = 1 : 2 : 3, then find the values of x, y and z.

1. 20°, 40°, 80°
2. 30°, 60°, 90°
3. 10°, 20°, 40°
4. 50°, 70°, 90°

Q. Find the values of the angles x, y and z in each of the following:

1. $x={115}^{\circ },y={140}^{\circ }andz={40}^{\circ }$
2. $x={215}^{\circ },y={10}^{\circ }andz={40}^{\circ }$
3. $x={125}^{\circ },y={190}^{\circ }andz={40}^{\circ }$
4. $x={175}^{\circ },y={120}^{\circ }andz={30}^{\circ }$

Q. If two lines intersect at a point, then the vertically opposite angles are always equal.

1. False
2. True

Q. When two lines intersect, the vertically opposite angles formed will be .

1. complementary
2. supplementary
3. adjacent
4. equal

Q. Find the value y if m || n and l is the transversal.

1. ${70}^{\circ }$
2. ${110}^{\circ }$
3. ${60}^{\circ }$
4. ${40}^{\circ }$

Q.

Question 81(iii)

Two angles have a common vertex and their arms form opposite rays (figure). Then
Write all the pairs of vertically opposite angles

Q. How to prove that vertically opposite angles are equal

Q.

Question 117

In the given figure, find the measures of $\angle PON$ and $\angle NPO$

Q.

Question 136

In the given figure, if RP = RQ, find the value of x.

Q.

Question 25

In the given figure $\angle AOC$ and $\angle BOC$ form a pair of

(a) vertically opposite angles
(b) complementary angles
(c) alternate interior angles
(d) supplementary angles

Q.

Question 73

In each of the following figures, write, if any (i) each pair of vertically opposite angles, and (ii) each linear pair.

Q.

Question 137

In the given figure, if ST = SU, then find the values of x and y.

Q.

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

1. $\angle$AOB = 150${}^{\circ }$

2. $\angle$BOC = 40${}^{\circ }$

3. $\angle$AOB = 15${}^{\circ }$

4. None of the above

Q. A projectile is fired at an angle of 45^°with the horizontal . What is the elevation angle of the projectile at its highest point as seen from the point of projection?

Q.

If two angles are complementary, then the sum of their measure is _____ .

Q.

Question 3 (iii)
Identify which of the following pairs of angles are complementary and which are supplementary:
${112}^{\circ },{68}^{\circ }$

Q.

In the figure below, lines AB and CD intersect each other at point O. Angles ($\angle$ 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 given figure, PQRS is a rectangle if $\angle RPQ={30}^{\circ }$. Then, the value of (x + y) is:

1. ${90}^{\circ }$

2. ${120}^{\circ }$

3. ${150}^{\circ }$

4. ${180}^{\circ }$