Question

PLEASE HELP ME GUYS!! Write and solve equations based on the angle relationships in the diagram below to find the measure of ∠EKC and ∠CKA

Answer 1

x = 65°

y = 25° (equations in explanation)

Explanation:

We know that EKD is 25° and we know that DKB is 90°.

EKD, DKB, and BKF are supplementary. This means that their angle measures add up to 180°.

So, since we know two, we can find the other very easily.

`180 - (25+90)\\180 - 115\\65`

This means that BKF is 65°.

Now, BKF and EKC are alternate interior angles, so they have the exact same measurement. Therefore, EKC, x, is 65°.

Again, EKC, CKA, and AKF are supplementary. AKF is 90° and EKC is 65°, so we can find the measure of CKA easily.

`180 - (65+90)\\180-155\\25`

Therefore y is 25° and x is 65°.

Hope this helped!