Question

If p ll q, m <7= 131°, and m<16 = 88°, find the measure of each missing angle.

Answer 1

Step-by-step explanation:

1.

Angles 7 and 5 are corresponding, then

Angles 7 and 2 are supplementary, then

Angles 1 and 7 are vertical, so

Angles 2 and 8 are vertical, so

Angles 2 and 4 are corresponding, then

Angles 1 and 3 are corresponding, then

Angles 8 and 6 are corresponding, then

Answer 2

Answer:

$m\angle 1=m\angle 3=m\angle 5=m\angle 7=131^{\circ}$

$m\angle 2=m\angle 4=m\angle 6=m\angle 8=49^{\circ}$

$m\angle 9=m\angle 11=m\angle 13=m\angle 15=92^{\circ}$

$m\angle 10=m\angle 12=m\angle 14=m\angle 16=88^{\circ}$

Step-by-step explanation:

1.

Angles 7 and 5 are corresponding, then

$m\angle 5=m\angle 7=131^{\circ}$

Angles 7 and 2 are supplementary, then

$m\angle 2=180^{\circ}-131^{\circ}=49^{\circ}$

Angles 1 and 7 are vertical, so

$m\angle 1=m\angle 7=131^{\circ}$

Angles 2 and 8 are vertical, so

$m\angle 2=m\angle 8=49^{\circ}$

Angles 2 and 4 are corresponding, then

$m\angle 2=m\angle 4=49^{\circ}$

Angles 1 and 3 are corresponding, then

$m\angle 1=m\angle 3=131^{\circ}$

Angles 8 and 6 are corresponding, then

$m\angle 6=m\angle 8=49^{\circ}$

Thus,

$m\angle 1=m\angle 3=m\angle 5=m\angle 7=131^{\circ}$

$m\angle 2=m\angle 4=m\angle 6=m\angle 8=49^{\circ}$

2.

Angles 16 and 14 are corresponding, then

$m\angle 16=m\angle 14=88^{\circ}$

Angles 16 and 15 are supplementary, then

$m\angle 15=180^{\circ}-88^{\circ}=92^{\circ}$

Angles 16 and 10 are vertical, so

$m\angle 10=m\angle 16=88^{\circ}$

Angles 9 and 15 are vertical, so

$m\angle 9=m\angle 15=92^{\circ}$

Angles 15 and 13 are corresponding, then

$m\angle 13=m\angle 15=92^{\circ}$

Angles 10 and 12 are corresponding, then

$m\angle 12=m\angle 10=88^{\circ}$

Angles 9 and 11 are corresponding, then

$m\angle 9=m\angle 11=92^{\circ}$

Thus,

$m\angle 9=m\angle 11=m\angle 13=m\angle 15=92^{\circ}$

$m\angle 10=m\angle 12=m\angle 14=m\angle 16=88^{\circ}$