Alternate Interior Angles

Q.

In the figure, if $PQ\parallel RS,\angle MXQ={135}^{\circ }$ and $\angle MYR={40}^{\circ }$, find $\angle XMY$.

1. ${75}^{\circ }$

2. ${40}^{\circ }$

3. ${65}^{\circ }$

4. ${85}^{\circ }$

Q. Identify the pairs of alternate interior angles for the given figure.

1. $\angle APF$ and $\angle EOD$
2. $\angle COE$ and $\angle EOD$
3. $\angle BPF$ and $\angle COE$
4. $\angle APF$ and $\angle COE$

Q.

In the figure given below, the measure of x is:

1. 40^o

2. 60^o

3. 30^o

4. 50^o

Q.

In the fig. below, if AB || CD, $\angle$APQ = 50${}^{\circ }$ and $\angle$PRD = 127${}^{\circ }$, find x and y.

​

1. x = 50${}^{\circ }$

2. y = 77${}^{\circ }$

3. y = 87${}^{\circ }$

4. x = 60${}^{\circ }$

Q.

In the given figure, for what value of 'x' will AB || CD?

1. ${87}^{\circ }$

2. ${63}^{\circ }$

3. ${19}^{\circ }$

4. ${29}^{\circ }$

Q.

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

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

2. 57${}^{\circ }$

3. 34${}^{\circ }$

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

Q. Find the angle ∠a for the below figure.

degrees.



Here the parallel lines are shown by arrow marks.

Q.

Question 46

Fill in the blanks to make the statement true.

Alternate interior angles have one common __.

Q. Activity-
(1)In the figure below, there is a pair of parallel lines and a third line cutting across them. In the figure, a measure of one angle is given and another angle is marked. Find out its measure and write it in the figure itself. (2 marks)

(2) In the figure below, there is a pair of parallel lines and a third line cutting across them. In the figure, a measure of one angle is given and another angle is marked. Find out its measure and write it in the figure itself.

Q. Find the angle $\angle HGE$ for the given figure using corresponding angles and alternate interior angles. Given $\angle DAB={105}^o.$
Here $AB\parallel DE\parallel HG\&AD\parallel BH\parallel GE$

1. ${15}^o$
2. ${105}^o$
3. None of the above.
4. Insufficient data.

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

Q. are the angles which lie inside of the two parallel lines but on alternate sides of the transversal.

Q. The measure of an exterior angle is equal to __ of two opposite interior angles.

1. product
2. sum
3. difference
4. division

Q.

In Figure, if $ AB\parallel CD\parallel EF$, $ PQ\parallel RS$, $ \angle RQD=25°$ and $ \angle CQP=60°$, then $ \angle QRS$ is equal to

Q. In the given figure $PQ$ ∥ $XY$ ∥ $RS$. Also, $y$ : $z$ = $4$ : $5$, then the values of $\angle x$, $\angle y$ and $\angle z$ are (respectively).

1. ${80}^{\circ },{80}^{\circ },{100}^{\circ }$
2. ${100}^{\circ },{80}^{\circ },{100}^{\circ }$
3. ${80}^{\circ },{100}^{\circ },{100}^{\circ }$

Q.

In the given figure AB is parallel to ED. If $\angle ABC={50}^{\circ }$ and $\angle EDC={40}^{\circ }$

then find the value of a and b.

1. $a={90}^{\circ }andb={270}^{\circ }$

2. $a={290}^{\circ }andb={70}^{\circ }$

3. $a={270}^{\circ }andb={90}^{\circ }$

4. $a={250}^{\circ }andb={110}^{\circ }$

Q. The measure of an exterior angle is equal to __ of two opposite interior angles.

1. product
2. sum
3. difference
4. division

Q. Which of the following show $x\&y$ as alternate interior angle?

1. 
2. 
3. 
4. Both (a) and (c)

Q.

In the figure, ACE, BCF and DCH are straight lines and AB || HC.

Find the angles p, q, r and s.

1. $p={45}^{\circ },q={50}^{\circ },r={65}^{\circ },s={50}^{\circ }$

2. $p={45}^{\circ },q={65}^{\circ },r={50}^{\circ },s={50}^{\circ }$

3. $p={45}^{\circ },q={65}^{\circ },r={50}^{\circ },s={65}^{\circ }$

4. $p={45}^{\circ },q={50}^{\circ },r={65}^{\circ },s={65}^{\circ }$

Q. What is the value of x in degrees?

1. 72
2. 45
3. 34
4. 68

Q.

In the given figure

If $l\parallel m$ then $\angle 3=\_\_\_\_$

Q.

In the given figure AB is parallel to ED. If $\angle ABC={50}^{\circ }$ and $\angle EDC={40}^{\circ }$

then find the value of a and b.

1. $a={90}^{\circ }andb={270}^{\circ }$

2. $a={290}^{\circ }andb={70}^{\circ }$

3. $a={270}^{\circ }andb={90}^{\circ }$

4. $a={250}^{\circ }andb={110}^{\circ }$

Q.

In the fig. below, if AB || CD, $\angle$APQ = 50${}^{\circ }$ and $\angle$PRD = 127${}^{\circ }$, find x and y.

​

1. 50${}^{\circ }$, 67${}^{\circ }$

2. 50${}^{\circ }$, 77${}^{\circ }$

3. 77${}^{\circ }$, 87${}^{\circ }$

4. 77${}^{\circ }$, 97${}^{\circ }$

Q. In the given figure, AB || CD, then the value of x is

​

1. ${285}^{\circ }$
2. ${235}^{\circ }$
3. ${75}^{\circ }$
4. ${220}^{\circ }$

Q.

If AB and CD are parallel, find the measure of angle x

1. 15°

2. 105°

3. 21°

4. 51°

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

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

Q.

If two interior angles on the same side of a transversal are in the ratio 4:5, then the smaller angle is

1. 40°

2. 80°

3. 60°

4. 100°

Q.

In the given figure, AB || DE. ∠A = 43⁰ and ∠BDE = 57⁰. The value of ∠x is ________.

1. 43${}^{\circ }$
2. 57${}^{\circ }$
3. 34${}^{\circ }$
4. 75${}^{\circ }$