### Home > GC > Chapter 6 > Lesson 6.1.3 > Problem 6-24

Use your conjectures about parallel lines and the angles formed with a third line to find the measures of the labeled angles below. Show each step you use and be sure to

**justify**each with an angle conjecture from your Angle Relationships Toolkit. Be sure to write down your**reasoning**in the order that you find the angles. Homework Help ✎

There are multiple correct ways to find the angle measures.

If parallel lines are cut by a transversal, then

corresponding angles have equal measures.

Vertical angles must also have equal measures.

The 123° angle corresponds to which angle?

∠*a* = 123° because corresponding angles on parallel lines have equal measures.

∠*a* = ∠*b* because

vertical angles have equal measures.

∠*c* + 123° =180°

because they are supplementary angles.

So what is ∠*c* ?

∠*a* = 123°, ∠*b* = 123°, °*c* = 57°

∠*d* = 98°, ∠*e* = 98°, ∠*f* = 98°

Make sure you write down your reasoning.