Question

Find the measure of angle MKN.

Answer 1

61

Explanation:

Since JKL is a straight line, it equals 180

JKM + MKN + NKL = 180

3x+2 + 6x+7 + 90 = 180

Combine like terms

9x+99 = 180

Subtract 99 from each side

9x+99-99= 180-99

9x =81

Divide each side by 9

9x/9 = 81/9

x=9

We want MKN

6x+7 = 6*9 +7 = 54+7 = 61

Answer 2

m∠MKN = 61°

Explanation:

Since KN is a perpendicular bisector, m∠NKM and m∠MKJ have to add up to 90°.

Step 1: Set up equation

6x + 7 + 3x + 2 = 90

Step 2: Solve for x

1. Combine like terms: 9x + 9 = 90
2. Subtract 9 on both sides: 9x = 81
3. Divide both sides by 9: x = 9

Step 3: Find m∠MKN

m∠MKN = 6x + 7

m∠MKN = 6(9) + 7

m∠MKN = 54 + 7

m∠MKN = 61°