SOLUTION: If DE and BC are parallel, angle 3 = angle 4 = 2(angle 2) and angle 6 = angle 2 + 12 degrees, find the measure of angle 1. file:///C:/Users/Chris/Downloads/Scanned%20Documents%2

Algebra ->  Geometry-proofs -> SOLUTION: If DE and BC are parallel, angle 3 = angle 4 = 2(angle 2) and angle 6 = angle 2 + 12 degrees, find the measure of angle 1. file:///C:/Users/Chris/Downloads/Scanned%20Documents%2      Log On


   

Question 1154687: If DE and BC are parallel, angle 3 = angle 4 = 2(angle 2) and angle 6 = angle 2 + 12 degrees, find the measure of angle 1.
file:///C:/Users/Chris/Downloads/Scanned%20Documents%20(2).pdf
*ignore black line down middle*
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
DE and BC are parallel,
< 3 = < 4 = 2*< 2
from the graph we see that
<+1= < 5 + <6+ as corresponding angles
< 5 = < 2 as alternate interior angles

if < 3 = < 4 = 2*< 2, < 5 = < 2 , and if < 2 is x
their sum is

< 2=36° and m < 5=36°
m< 3 = m< 4 = 2*< 36=72°

and if m < +6 = < 2 + 12° , we have
m < +6 = 12%2B36= 48°
m < DEB=180-%2848%2B36%29=96°
m< +1= 36%2B48°= 84°

so, m< +1= 84°

check if the sum of m < DEB%7D%7D+and+%7B%7B%7Bm< +1 is 180°

m < DEB%7D%7D+%2B+%7B%7B%7Bm< +1=96%2B84°=180°