Question

If ∠MOK and ∠JOM are supplementary angles, then what is the value of x and m∠LOK?

A.
x = 130; m∠LOK = 66°
B.
x = 50; m∠LOK = 114°
C.
x = 114; m∠LOK = 50°
D.
x = 66; m∠LOK = 130°

Answer 1

B

Explanation:

Note that angle JOM and angle LOK are vertical angles meaning that they are congruent ( equal to each other )

We are given that angle MOK and angle JOM are supplementary

Supplementary angles add up to 180

This means that:

angle MOK + angle JOM = 180

If angle JOM = angle LOK

Then angle MOK + angle LOK also = 180

If angle MOK = 66 and angle LOK = x + 64

Then 66 + x + 64 = 180

Note that we've just created an equation that we can use to solve for x

We now solve for x

66 + x + 64 = 180

Combine like terms

66 + 64 = 130

130 + x = 180

Subtract 130 from both sides

x = 50

We also want to find the measure of angle LOK.

To do so we simply plug in the value of x into x + 64

angle LOK = x + 64

x = 50

angle LOK = 50 + 64 = 114

So x = 50 and angle LOK = 114

Hence the answer is B