Question

lines ( l_1 ), and ( l_2 ) are parallel lines. determine the measures of ( angle 1 ) through ( angle 12 )

( mangle 7 = 56^circ )
( mangle 1 = 56^circ )
( mangle 2 = 56^circ )
( mangle 3 = 56^circ )
( mangle 4 = 66^circ )
( mangle 5 = 56^circ )
( mangle 6 = 114^circ )
( mangle 8 = 114^circ )

Explanation:

Step1: Identify given angle

$m\angle 7 = 56^\circ$ (given)

Step2: Find $\angle 1$ (corresponding angles)

$\angle 1$ and $\angle 7$ are corresponding angles, so $m\angle 1 = m\angle 7 = 56^\circ$

Step3: Find $\angle 2$ (vertical to $\angle 7$)

$\angle 2$ and $\angle 7$ are vertical angles, so $m\angle 2 = m\angle 7 = 56^\circ$

Step4: Find $\angle 3$ (supplementary to $\angle 7$)

$\angle 3$ and $\angle 7$ are same-side interior angles, so $m\angle 3 = 180^\circ - 56^\circ = 124^\circ$

Step5: Find $\angle 4$ (supplementary to $\angle 1$)

$\angle 4$ and $\angle 1$ are supplementary, so $m\angle 4 = 180^\circ - 56^\circ = 124^\circ$

Step6: Find $\angle 5$ (vertical to $\angle 1$)

$\angle 5$ and $\angle 1$ are vertical angles, so $m\angle 5 = m\angle 1 = 56^\circ$

Step7: Find $\angle 6$ (corresponding to $\angle 3$)

$\angle 6$ and $\angle 3$ are corresponding angles, so $m\angle 6 = m\angle 3 = 124^\circ$

Step8: Find $\angle 8$ (supplementary to $\angle 7$)

$\angle 8$ and $\angle 7$ are supplementary, so $m\angle 8 = 180^\circ - 56^\circ = 124^\circ$

Step9: Find $\angle 9$ (vertical to $\angle 7$)

$\angle 9$ and $\angle 7$ are vertical angles, so $m\angle 9 = m\angle 7 = 56^\circ$

Step10: Find $\angle 10$ (vertical to $\angle 8$)

$\angle 10$ and $\angle 8$ are vertical angles, so $m\angle 10 = m\angle 8 = 124^\circ$

Step11: Find $\angle 11$ (vertical to $\angle 7$)

$\angle 11$ and $\angle 7$ are vertical angles, so $m\angle 11 = m\angle 7 = 56^\circ$

Step12: Find $\angle 12$ (vertical to $\angle 6$)

$\angle 12$ and $\angle 6$ are vertical angles, so $m\angle 12 = m\angle 6 = 124^\circ$

Answer:

$m\angle 1 = 56^\circ$
$m\angle 2 = 56^\circ$
$m\angle 3 = 124^\circ$
$m\angle 4 = 124^\circ$
$m\angle 5 = 56^\circ$
$m\angle 6 = 124^\circ$
$m\angle 7 = 56^\circ$
$m\angle 8 = 124^\circ$
$m\angle 9 = 56^\circ$
$m\angle 10 = 124^\circ$
$m\angle 11 = 56^\circ$
$m\angle 12 = 124^\circ$