Question

Find mZA and mZB.
Please help :)

Answer 1

Angle A: 28 degrees

Angle B: 24 degrees

Explanation:

Hi there!

The angle that measures 52 degrees (angle DCA) is one of the exterior angles of a triangle. An exterior angle of a triangle is equal to the sum of the opposite interior angles, which in this case would be angles A and B. Knowing this, we can set up the following equation:

`4y-4+3y=52`

1) Solve for y

`4y-4+3y=52`

Combine like terms

`7y-4=52`

Add 4 to both sides to isolate 7y

`7y-4+4=52+4\\7y=56`

Divide both sides by 7

`(7y)/(7)=(56)/(7) \\y=8`

Therefore, y is equal to 8.

2) Solve for angles A and B

Angle A:

`4y-4\\=4(8)-4\\=32-4\\=28`

Angle B:

`3y\\=3(8)\\=24`

I hope this helps!