Alternate Interior and Exterior Angles

Q. When a transversal intersects two non parallel lines, then the alternate interior angles are _____.

1. equal
2. always supplementary
3. unequal
4. always complementary

Q. In the following figure, $l_1,l_2,l_3$ are parallel to each other. Find the value of $\angle BDC\text{if}\angle BFE=\angle BCD={50}^{\circ }.$

1. 80°
2. 90°
3. 50°
4. 40°

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. ${60}^{\circ }$

2. ${30}^{\circ }$

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

4. ${90}^{\circ }$

Q.

In the given figure, AB || DE.
$\angle A={43}^{\circ }and\angle BDE={57}^{\circ }$.
The value of x is ________.

1. 57

2. 75

3. 43

4. 34

Q.

In the figure a pair of parallel lines are cut by a transversal. Find the value of a and b respectively.

1. ${72}^{\circ },{47}^{\circ }$

2. ${72}^{\circ },{72}^{\circ }$

3. ${62}^{\circ },{62}^{\circ }$

4. ${57}^{\circ },{62}^{\circ }$

Q.

In the figure a pair of parallel lines are cut by a transversal. Find the value of a and b respectively.

1. ${72}^{\circ },{72}^{\circ }$

2. ${72}^{\circ },{47}^{\circ }$

3. ${62}^{\circ },{62}^{\circ }$

4. ${57}^{\circ },{62}^{\circ }$

Q. If two lines and a transversal form corresponding angles that are equal, then the lines are parallel.

1. False
2. True

Q. In the given figure, AB || CD. If ∠BPR = k°, ∠RPQ = 70° and ∠PQC = 130°, find the value of k.

1. 70
2. 130
3. 40
4. 60

Q.

In the given figure, AB || DE. $\angle$A = 43${}^{\circ }$ and $\angle$BDE = 57${}^{\circ }$. The value of $\angle$B is ________.

1. 43${}^{\circ }$

2. 34${}^{\circ }$

3. 57${}^{\circ }$

4. 75${}^{\circ }$

Q.

State the property used in each of the following statements in context of the figure given here

If $a\parallel b$ then $\angle 3+\angle 6=180°$.

Q.

State the property used in each of the following statements in context of the figure given here

If $\angle 4+\angle 5=180°$ then $a\parallel b$.

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

1. 115°
2. 110°
3. 105°
4. 95°

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

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

Q. In the given figure, if AB || CD || EF,
PQ || RS, $\angle RQD=25°\text{and}\angle CQP=60°$, then find $\angle QRS$ .

1. 140°
2. 145°
3. 135°
4. 130°

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 two parallel lines l, m are intersected by a tranversal. If $\angle 4={45}^{\circ }$ then $\angle 3$ and $\angle 6$ are

1. $\angle 3={135}^{\circ }$

2. $\angle 3={145}^{\circ }$

3. $\angle 6={75}^{\circ }$

4. $\angle 6={45}^{\circ }$