Interior Angle Theorem

Q.

If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

1. True

2. False

Q.

Statements a and b are as given below:

a: If two lines intersect, then the vertically opposite angles are equal.

b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is $180°$.

1. Both $a$ and $b$ are true

2. $a$ is true and $b$ is false

3. $a$ is false and $b$ is true

4. both $a$ and $b$ are false

Q.

In the given figure AB||CD.
If $\angle CDE={85}^{\circ }$, then find the value of x and y respectively.

1. ${95}^{\circ },{85}^{\circ }$

2. ${85}^{\circ },{95}^{\circ }$

3. ${90}^{\circ },{90}^{\circ }$

4. ${105}^{\circ },{75}^{\circ }$

Q.

In the adjoining figure, AB is parallel to CD. Find the value of x.

1. 80${}^{\circ }$

2. 88${}^{\circ }$

3. 90${}^{\circ }$

4. 98${}^{\circ }$

Q. If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then the measure of the larger angle is

(a) 54°

(b) 120°

(c) 108°

(d) 136°

Q. If one of cointerior angles is 60 degrees then the other angle is equal to ____ degrees

1. 30
2. 60
3. 120
4. 150

Q.

Fill in the blanks :

If two parallel lines are cut by a transversal, then each pair of alternate angles is ……………..

Q. Fill in the blanks in each of the following to make the statement true:

(i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are ...
(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ....
(iii) Two lines perpendicular to the same line are ... to each other.
(iv) Two lines parallel to the same line are ... to each other.
(v) If a transversal intersects a pair of lines in such away that a pair of alternate angles are equal, then the lines are ...
(vi) If a transversal intersects a pair of lines in such away that the sum of interior angles on the same side of transversal is 180°, then the lines are ...

Q. In the given figure, it is given that line ABDE is a straight line and AE || PQ . FInd $\angle$PCB and $\angle$QCD.

1. ${110}^{\circ }$, ${100}^{\circ }$
2. ${70}^{\circ }$, ${80}^{\circ }$
3. ${60}^{\circ }$, ${30}^{\circ }$
4. ${45}^{\circ }$, ${45}^{\circ }$

Q. In the adjoining figure, ABCD is a parallelogram in which ∠BAO = 35°, ∠DAO = 40° and ∠COD = 105°. Calculate (i) ∠ABO, (ii) ∠ODC, (iii) ∠ACB, (iv) ∠CBD.

Q. In the given figure, ABCD is a cyclic quadrilateral in which AB || DC.
If ∠BAD = 100°, find
(i) ∠BCD (ii) ∠ADC (iii) ∠ABC.

Q. (i) If a transversal intersects two parallel lines then state the relation between alternate angles.
(ii) If each of the two parallel lines are parallel to the third line then what is the relation between them?
(iii) If a transversal intersects two parallel lines and the corresponding sides of two angles are parallel then what is the relation between these angles?
(iv) If AB is a line and P is a point outside it then how many lines can be drawn through P and Parallel to AB?
(v) If a transversal intersects two parallel lines such that the ratio between the interior angles on one of its side is 2:7, then find the measure of the greater angle.

Q.

In the figure, AB is parallel to CD, if $\angle 1+\angle 3={240}^{\circ }$, find the value of $\angle 6$.

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

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

3. ${90}^{\circ }$

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

Q.

In the adjoining figure, AB is parallel to CD. Find the value of x.

1. 80${}^{\circ }$

2. 88${}^{\circ }$

3. 90${}^{\circ }$

4. 98${}^{\circ }$

Q. AB || DE. Join AD and BD. If $\angle A={43}^{\circ }\text{and}\angle BDE={57}^{\circ }$, then $\angle ABD=$

1. 43${}^{\circ }$
2. 57${}^{\circ }$
3. 36${}^{\circ }$

Q.

In the figure shown, lines l and m are parallel and lines r and t are transversals. Find x.

1. ${45}^{\circ }$

2. ${75}^{\circ }$

3. ${60}^{\circ }$

4. ${105}^{\circ }$

Q.

In the given figure, Find the value of q.

1. ${48}^{\circ }$

2. ${90}^{\circ }$

3. ${42}^{\circ }$

4. ${110}^{\circ }$

Q.

It is given that, AB || DE. Find the value of y, if $\angle$ABC= ${110}^{\circ }$ and $\angle$CDE= ${100}^{\circ }$.

1. ${30}^{\circ }$

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

3. ${50}^{\circ }$

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

Q. Lines PQ and RS are parallel. It is given that $\angle RSP={52}^{\circ }$, then find $\angle SPQ$.

1. ${38}^{\circ }$
2. ${52}^{\circ }$
3. ${45}^{\circ }$
4. ${48}^{\circ }$

Q.

The sum of the co-interior angles is always ${180}^{\circ }$.

1. False

2. True

Q. In the given figure, AB || CD and O is a point joined with B and D, as shown in the figure, such that ∠AOB = 35° and ∠CDO = 40°. What will be the measure of reflex ∠BOD ?
(a) 225°
(b) 265°
(c) 275°
(d) 285°

Q.

Find the measure of $\angle ADC$ in the given figure.

1. ${45}^{\circ }$

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

3. ${30}^{\circ }$

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

Q. It is given that, AB || DE. Find the value of y, if $\angle ABC={110}^{\circ }$ and $\angle CDE={100}^{\circ }$.

Q.

Which one of the following is not correct?

1. If two parallel lines are intersected by a transversal, then alternate angles are equal.

2. If two lines are intersected by a transversal then sum of the interior angles on the same side of transversal is 180${}^{\circ }$.

3. If two parallel lines are intersected by a transversal then corresponding angles are equal.

4. Two parallel lines never meet.