Alternate Interior Angles Theorem

Q. Find the value of x in the following figure, if the lines l & m are parallel to each other.

1. $x={90}^{\circ }$
2. $x={80}^{\circ }$
3. $x={60}^{\circ }$
4. $x={70}^{\circ }$

Q. The two lines are parallel and are cut by a transversal. Find the value of x.

1. 17°
2. 34°
3. 57°
4. 74°

Q. In the given figure, PQ || RS. Find the values of a, b and c.

1. 20°, 40°, 120°
2. 30°, 50°, 100°
3. 10°, 60°, 110°
4. 15°, 55°, 110°

Q.

In the given figure, find the value of $\angle BAC$. $\Delta DEF$ is equilateral, $\angle CBA={40}^{\circ }$, $\angle FEC={50}^{\circ }$ and DE is parallel to BC. [4 MARKS]

Q. In the figure, AO and CD are parallel to YZ. Find the value of x.

1. 45°
2. 60°
3. 65°
4. 40°

Q.

Find the value of $\angle 1$ (in degrees).
Given, l and m are two parallel lines.

1. 105

2. Can’t say

3. 120

4. 100

Q. Find the value of $\angle$ 1 if the two parallel lines are cut by a transversal.

1. 65°
2. 115°
3. 100°
4. 135°

Q. In the given figure, find whether $l$ is parallel to m.

Q.

Question 28

In which of the following figures, a and b are forming a pair of adjacent angles?

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Q.

Question 133

In the given figure, $\Delta PQR$ is the right-angled at P. U and T are the points on the line QR. If $QP\parallel ST$ and $US\parallel RP$, find $\angle S$

Q. If M || N and L is the transversal, then $\angle x$ will be ____.

1. 105°
2. 95°
3. 115°
4. 110°

Q. Find the measure of x, if ZY || WX in the following figure.

1. ${112}^{\circ }$
2. ${56}^{\circ }$
3. ${68}^{\circ }$
4. ${106}^{\circ }$

Q. In the figure, AO and CD are parallel to YZ. Find the value of x.

1. 40°
2. 45°
3. 65°
4. 60°

Q. Find the alternate interior angles.

1. $\angle$1 and $\angle$7
2. $\angle$4 and $\angle$6
3. $\angle$2 and $\angle$8
4. $\angle$3 and $\angle$5

Q.

In the given figure, if AB || CD, then find the value of x.

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1. ${275}^{\circ }$

2. ${285}^{\circ }$

3. ${235}^{\circ }$

4. ${220}^{\circ }$

Q. Find the value of x, y, and z when l || BC .

1. x = 75°, y = 45° and z = 60°.
2. x = 60°, y = 45° and z = 75°.
3. x = 60°, y = 75° and z = 45°.
4. x = 45°, y = 75° and z = 60°.

Q.

In the given diagram, AB is parallel to PQ. If a right triangle can be constructed with $\angle P{O}^{\prime }X$ and $\angle BOY$ as two of its angles, then find the value of $\angle P{O}^{\prime }X$.

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

2. ${60}^{\circ }$

3. ${45}^{\circ }$

4. ${30}^{\circ }$