Question

Using what you know about angles and translations, find all of the angle

measures in the image below.
.
<1 = 135°
<2 =
<3 =
<4 =
<5 =
<6 =
<7 =
<8 =
Explain how you found the measure of <8.

Answer 1

angle 8 is the same as angle 1.

Explanation:

opposite side exterior angles are congruent

Answer 2

2=45, 3=45, 4=135, 5=135, 6=45, 7=135, 8=135

Explanation:

Assuming that these lines are parallel, alternate interior angles are supplementary and alternate exterior angles are also supplementary. So, we know that 1=135 so that means we can do 180-135=45 so 2=45. 1 and 4 are equal to each other because of the vertical angle theorem. So every angle is either 45 degrees or 135 degrees. So:

2=3=6=7

1=4=5=8

You can use the theorems to figure out which angles are congruent and which angles are supplementary in a transversal.

I hope this makes sense