Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).

in the figure, transversal t intersects the parallel lines a and b, and ( mangle1 ) is ( 64.76^{circ} ).

( mangle4 ) is

( mangle6 ) is

Explanation:

Step1: Find \( m\angle4 \)

Since \( \angle1 \) and \( \angle4 \) are supplementary (they form a linear - pair), \( m\angle1+m\angle4 = 180^{\circ} \).
Given \( m\angle1=64.76^{\circ} \), then \( m\angle4=180 - 64.76\).
\( m\angle4 = 115.24^{\circ} \).

Step2: Find \( m\angle6 \)

Since lines \( a\parallel b\) and \( t\) is a transversal, \( \angle4\) and \( \angle6\) are alternate - interior angles.
By the alternate - interior angles theorem (if two parallel lines are cut by a transversal, then alternate - interior angles are congruent), \( m\angle6=m\angle4\).
So \( m\angle6 = 115.24^{\circ} \).

Answer:

\( m\angle4 = 115.24\), \( m\angle6 = 115.24\)