Let's solve each of the problems step by step using
angle properties formed by parallel lines and transversals. Key concepts include:
-
Vertical angles are equal.
-
Corresponding angles are equal when lines are parallel.
-
Alternate interior angles are equal.
-
Alternate exterior angles are equal.
-
Supplementary angles (on a straight line) add up to 180°.
-
Consecutive interior angles (same-side interior) are supplementary.
---
1.
Two parallel lines cut by a transversal. One angle is 72°, and we're finding angle $ x $, which is
vertically opposite to the 72° angle.
✔ Vertical angles are equal, so:
$$
x = 72^\circ
$$
---
2.
We have two intersecting lines forming an angle of 48°. The angle marked $ x $ is
opposite to this 48° angle.
✔ Vertical angles are equal:
$$
x = 48^\circ
$$
---
3.
Two intersecting lines with one angle given as 60°. The angle $ x $ is
adjacent to it on a straight line.
✔ Adjacent angles on a straight line sum to 180°:
$$
x = 180^\circ - 60^\circ = 120^\circ
$$
---
4.
Parallel lines cut by a transversal. One angle is 55°, and $ x $ is
corresponding to that angle.
✔ Corresponding angles are equal:
$$
x = 55^\circ
$$
---
5.
Two intersecting lines form a 96° angle. The angle $ x $ is
vertical to it.
✔ Vertical angles are equal:
$$
x = 96^\circ
$$
---
6.
Two vertical parallel lines, a transversal cuts them. One angle is 105°, and $ x $ is
corresponding to it.
✔ Corresponding angles are equal:
$$
x = 105^\circ
$$
---
7.
We have two parallel lines and a transversal. One angle is 131°, and $ x $ is
alternate interior or
supplementary depending on position.
Looking at the diagram: The 131° angle and $ x $ are
on the same side of the transversal and between the parallel lines → they are
consecutive interior angles, so they are
supplementary.
$$
x = 180^\circ - 131^\circ = 49^\circ
$$
---
8.
Parallel lines with a transversal. One angle is 112°, and $ x $ is
alternate interior to it.
✔ Alternate interior angles are equal:
$$
x = 112^\circ
$$
---
9.
This one is a bit more complex. We have two parallel lines and a transversal. One angle is 147°, and $ x $ is adjacent to it on a straight line.
First, find the angle
adjacent to 147°:
$$
180^\circ - 147^\circ = 33^\circ
$$
Now, this 33° angle is
corresponding to $ x $ (since the lines are parallel), so:
$$
x = 33^\circ
$$
Alternatively, you can think: $ x $ is
alternate interior to the 33° angle, but since it’s corresponding, same result.
✔ So,
$$
x = 33^\circ
$$
---
✔ Final Answers:
1. $ x = 72^\circ $
2. $ x = 48^\circ $
3. $ x = 120^\circ $
4. $ x = 55^\circ $
5. $ x = 96^\circ $
6. $ x = 105^\circ $
7. $ x = 49^\circ $
8. $ x = 112^\circ $
9. $ x = 33^\circ $
Let me know if you'd like diagrams labeled for clarity!
Parent Tip: Review the logic above to help your child master the concept of angles in transversal worksheet answer key.
