Properties of Angles Formed by Two Parallel Lines and a Transversal

Q.

When two lines are cut by a transversal and their alternate interior angles are equal, then the lines are

1. perpendicular

2. parallel

3. inclined at 120 degrees

4. inclined at 60 degrees

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

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

Q. The sum of co interior angles when a transversal cuts a pair of parallel lines is __________.

1. 270 degrees
2. 180 degrees
3. 360 degrees
4. 90 degrees

Q. If A and B are alternate interior angles and A = 78 degrees, then B = ___ degrees.

1. 12
2. 78
3. 282
4. 102

Q. The sides BA and DC of the parallelogram ABCD are produced as shown in figure. Then

1. $\angle a=\angle x+\angle y$
2. $\angle a=\angle b=(\angle x+\angle y)$
3. $\angle y=\angle a-\angle b$
4. $\angle a+\angle b=\angle x+\angle y$

Q.

Two lines are cut by a transversal and interior angles on same side are supplementary, the lines are

1. parallel

2. perpendicular

3. inclined at 120 degrees

4. have no relation

Q. In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, then find x.

1. ${112}^{\circ }$
2. ${116}^{\circ }$
3. ${96}^{\circ }$
4. ${126}^{\circ }$

Q.

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

Find the angles p, q, r and s.

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

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

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

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

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 given figure if line AB is parallel to line CD then which of the following are true?

1. $\angle AQX=\angle CPY$

2. $\angle BQX=\angle DPX$

3. $\angle AQP=\angle CPQ$

4. $\angle BQP=\angle CPY$