Question

part b find the angle measures if ( mangle1 = 60^circ ). ( mangle7 = ) ( ^circ ) ( mangle8 = ) ( ^circ ) ( mangle9 = ) ( ^circ ) alternate interior angles corresponding angles vertical angles ( angle7 ) and ( angle9 ) ( angle1 ) and ( angle7 ) ( angle4 ) and ( angle11 )

Explanation:

Step1: Use Corresponding Angles Property

$\angle 1$ and $\angle 7$ are corresponding angles, so $m\angle 7 = m\angle 1 = 60^\circ$

Step2: Use Alternate Interior Angles Property

$\angle 7$ and $\angle 9$ are alternate interior angles, so $m\angle 9 = m\angle 7 = 60^\circ$

Step3: Note $\angle 8$ supplementary to $\angle 7$

$\angle 7$ and $\angle 8$ form a linear pair, so $m\angle 8 = 180^\circ - m\angle 7 = 180^\circ - 60^\circ = 120^\circ$

Answer:

$m\angle 7 = 60^\circ$
$m\angle 8 = 120^\circ$
$m\angle 9 = 60^\circ$