**Definition of Corresponding Angle Conjecture**

- If two parallel lines are cut by a transversal, then the Corresponding Angles are congruent.

**More about Corresponding Angle Conjecture**

- If a transversal intersects two lines and the corresponding angles are congruent, then the lines are parallel.

**Example of Corresponding Angle Conjecture**

- In the above figure, CG||DH and AF is the transversal cutting the two parallel lines. The pairs of corresponding angles ∠ABC and ∠BED, ∠CBE and ∠DEF, ∠ABG and ∠BEH, and ∠GBE and ∠HEF are equal.

**Solved Example on Corresponding Angle Conjecture**

landmare parallel lines in the figure. What are the measures of ∠x, ∠y, and ∠z?

Choices:

A. 60°, 30° and 30°

B. 30°, 30° and 32°

C. 58°, 32° and 32°

D. None of the above

Correct Answer: C

Solution:

Step 1:From the figure, ∠x and 58°, ∠y and ∠z form corresponding angles.

Step 2:∠x = 58° [Corresponding angles are equal.]

Step 3:∠z + 90° + 58° = 180°

Step 4:So, ∠z + 148° = 180°

Step 5:∠z = 180° - 148° = 32°

Step 6:∠z = ∠y [Corresponding angles are equal.]

Step 7:∠y = 32°

**Related Terms for Corresponding Angle Conjecture**

- Angle
- Congruent
- Corresponding Angle
- Parallel Lines
- Transversal