Question

39.
in the figure below, line ( m ) is parallel to line ( n ), and line ( t ) is a transversal crossing both ( m ) and ( n ). which of the following lists has 3 angles that are all equal in measure?
a. ( angle a,angle b,angle d )
b. ( angle a,angle c,angle d )
c. ( angle a,angle c,angle e )
d. ( angle b,angle c,angle d )
e. ( angle b,angle c,angle e )

Explanation:

Step1: Recall vertical - angle and parallel - line properties

Vertical angles are equal. When two parallel lines are cut by a transversal, corresponding angles are equal.

• $\angle a$ and $\angle c$ are vertical angles, so $\angle a=\angle c$.
• Since $m\parallel n$, $\angle a$ and $\angle d$ are corresponding angles, so $\angle a = \angle d$.

Answer:

B. $\angle a,\angle c,\angle d$