Alternate Interior Angle Theorem

Q.

What are co-interior angles?

Q.

Fill in the blanks :

If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are ………….

Q. From the diagram, if $AB$ and $CD$ are parallel to each other, then the value of reflex $\angle EOF$ is

1. ${210}^{\circ }$
2. ${210}^{\circ }$
3. ${235}^{\circ }$

Q. The alternate interior angles are congruent when the transversal intersects two parallel lines.

1. True
2. False

Q. Alternate interior angles are angles formed when two parallel or non-parallel lines are intersected by a transversal.

1. True
2. False

Q.

Find the value of 𝑥 and 𝑦 if RS is parallel to PQ.

Q. If AB and CD are parallel lines, what is the value of $x$ in the given figure?

Q.
For the diagram above, if $CD,PQ,RS$ are parallel to one another, then $\angle 4=$.

1. $\angle 10$
2. $\angle 9$
3. $\angle 11$

Q. Using alternate interior angles theorem, find $\angle a$ for the triangle in the image to be an equilateral triangle.
Given that the horizontal lines are parallel.

1. ${75}^o$
2. ${60}^o$

Q. Given that $l\parallel m\parallel n$ in the given figure.Find the value of $x$ and $y$

1. $x={30}^o\text{and}y={150}^o$
2. $x={40}^o\text{and}y={140}^o$
3. $x={50}^o\text{and}y={130}^o$
4. $x={60}^o\text{and}y={120}^o$

Q. Line $l||m$ and Line $p||q$ and two angles are given as ${45}^o\text{and}{75}^o$. Then value of $x+y$ is

1. ${30}^o$
2. ${100}^o$
3. ${120}^o$
4. None

Q. For the given diagram if the value of $\angle 2={108}^{\circ }$, then for $CD$ parallel to $PQ$, $\angle 5=$.

1. ${72}^{\circ }$
2. ${108}^{\circ }$
3. ${252}^{\circ }$

Q. For the diagram above, if $CD$ and $PQ$ are parallel to each other, then $\angle 3=$.

1. $\angle 4$
2. $\angle 5$
3. $\angle 8$

Q.
For the diagram shown above, $\angle 3\&$are alternate interior angles while $\angle 3\&$ co-interior angles.

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

Q. Line $p||q$, the value of $x$ is

1. ${30}^o$
2. ${40}^o$
3. ${20}^o$
4. None of the above

Q. In the given figure, $QP||RS.$ Find the values of a and b.