Question

1. ( a parallel b ). find all angle measures.

( mangle 1 = )
( mangle 2 = )
( mangle 3 = )
( mangle 4 = )
( mangle 5 = )
( mangle 6 = )
( mangle 7 = )

1. find the midpoint of ( overline{gh} ) with ( g(6, -2) ) and ( h(13, 10) ).

Explanation:

Step1: Find \( m\angle1 \)

\( \angle1 \) is given as \( 47^\circ \), so \( m\angle1 = 47^\circ \).

Step2: Find \( m\angle2 \)

\( \angle1 \) and \( \angle2 \) are supplementary (linear pair), so \( m\angle2 = 180^\circ - 47^\circ = 133^\circ \).

Step3: Find \( m\angle3 \)

\( \angle3 \) and \( \angle1 \) are corresponding angles (since \( a\parallel b \)), so \( m\angle3 = 47^\circ \).

Step4: Find \( m\angle4 \)

\( \angle4 \) and \( \angle1 \) are vertical angles, so \( m\angle4 = 47^\circ \).

Step5: Find \( m\angle5 \)

\( \angle5 \) and \( \angle2 \) are corresponding angles (since \( a\parallel b \)), so \( m\angle5 = 133^\circ \).

Step6: Find \( m\angle6 \)

\( \angle6 \) and \( \angle1 \) are alternate interior angles (since \( a\parallel b \)), so \( m\angle6 = 47^\circ \).

Step7: Find \( m\angle7 \)

\( \angle7 \) and \( \angle2 \) are vertical angles, so \( m\angle7 = 133^\circ \).

Answer:

\( m\angle1 = 47^\circ \), \( m\angle2 = 133^\circ \), \( m\angle3 = 47^\circ \), \( m\angle4 = 47^\circ \), \( m\angle5 = 133^\circ \), \( m\angle6 = 47^\circ \), \( m\angle7 = 133^\circ \)