Question

9 - 15. find the measure of each angle. use vocabulary to justify answer using angle vocabulary. you may need to use more than one term
( t parallel s ) ( mangle 2 = 107^circ ) ( mangle 6 = 64^circ )
( mangle 3 = ) ____ b/c ( angle 2 ) ____
( mangle 10 = ) ____ b/c ( angle 2 ) ____
( mangle 9 = ) ____ b/c ( angle 2 ) ____
( mangle 5 = ) ____ b/c ( angle 6 ) ____
( mangle 7 = ) ____ b/c ( angle 6 ) ____
( mangle 16 = ) ____ b/c ( angle 6 ) ____
( mangle 13 = ) ____ b/c ( angle 6 ) ____

Explanation:

Step1: Find $m\angle3$ (supplementary to $\angle2$)

$\angle2$ and $\angle3$ are supplementary (linear pair).
$m\angle3 = 180^\circ - m\angle2 = 180^\circ - 107^\circ = 73^\circ$

Step2: Find $m\angle10$ (corresponding to $\angle2$)

$\angle2$ and $\angle10$ are corresponding angles (since $t\parallel s$).
$m\angle10 = m\angle2 = 107^\circ$

Step3: Find $m\angle9$ (supplementary to $\angle10$)

$\angle9$ and $\angle10$ are supplementary (linear pair).
$m\angle9 = 180^\circ - m\angle10 = 180^\circ - 107^\circ = 73^\circ$

Step4: Find $m\angle5$ (supplementary to $\angle6$)

$\angle5$ and $\angle6$ are supplementary (linear pair).
$m\angle5 = 180^\circ - m\angle6 = 180^\circ - 64^\circ = 116^\circ$

Step5: Find $m\angle7$ (vertical to $\angle6$)

$\angle7$ and $\angle6$ are vertical angles.
$m\angle7 = m\angle6 = 64^\circ$

Step6: Find $m\angle16$ (corresponding to $\angle6$)

$\angle6$ and $\angle16$ are corresponding angles (since $t\parallel s$).
$m\angle16 = m\angle6 = 64^\circ$

Step7: Find $m\angle13$ (corresponding to $\angle5$)

$\angle5$ and $\angle13$ are corresponding angles (since $t\parallel s$).
$m\angle13 = m\angle5 = 116^\circ$

Answer:

$m\angle3 = 73^\circ$ (supplementary/linear pair with $\angle2$)
$m\angle10 = 107^\circ$ (corresponding angle to $\angle2$)
$m\angle9 = 73^\circ$ (supplementary/linear pair with $\angle10$)
$m\angle5 = 116^\circ$ (supplementary/linear pair with $\angle6$)
$m\angle7 = 64^\circ$ (vertical angle to $\angle6$)
$m\angle16 = 64^\circ$ (corresponding angle to $\angle6$)
$m\angle13 = 116^\circ$ (corresponding angle to $\angle5$)