Question

Lines m and n are parallel. They are cut by transversal t. What other angle is equal to 65 degrees?

1) 1
2) 2
3) 3
4) 4

Answer 1

To find another angle equal to 65 degrees formed by two parallel lines and a transversal, one must identify the angle corresponding or alternate interior to the given angle on the other parallel line cut by the transversal.

Step-by-step explanation:

When two parallel lines such as line m and line n are cut by a transversal like line t, several angles are formed that have specific relationships with each other. To find another angle that is equal to 65 degrees, we use the properties of parallel lines and transversals:

• Corresponding angles are equal.
• Alternate interior angles are equal.
• Alternate exterior angles are equal.
• Consecutive interior angles are supplementary (they add up to 180 degrees).

If an angle measures 65 degrees, the angles that are corresponding or alternate interior to it on the other parallel line cut by the transversal will also measure 65 degrees.