Question

The white trim shown for the wall of a barn should be constructed so the AC || EG, JA || HB,

and JC || KG. What should m<1 and m<3 be?

Answer 1

m∠1 = 112 degrees and m∠3 = 68 degrees

Explanation:

Using opposite interior angles;

The top portion is a parallelogram, which means that m∠F = 68 degrees since those two angles are opposite from each other.

m∠1:

You know that a parallelogram has 360 degrees, so

multiply the two known angles by 2 to get the sum of those angles,

subtract that value from 360 to get the sum of m∠1 and the unmarked angle,

then divide that difference by 2 to find the value of m∠1 and the unmarked angle -->

2(68) = 136 degrees,

360 - 136 = 224 degrees,

224/2 = 112 degrees

m∠1 = 112 degrees

m∠3:

Since JC is a straight (180 degree) line, m∠F and m∠3 are equivalent.

m∠3 = 68 degrees

Also, if you need it, m∠2 = 68 degrees as well since ∠2 and ∠F are opposite exterior angles across line EG.