Question

Angle M and Angle N are vertical angles. The measure of Angle M is 3x – 18. The measure of Angle N is x + 30.

Solve for x, and find the measures of Angles M and N.
x =
Measure of Angle M = degrees.
Measure of Angle N = degrees.

Answer 1

`24 = x`

`54° = Measure\:of\:Angle\:N`

`54° = Measure\:of\:Angle\:M`

Explanation:

Vertical Angles are congruent, so set the two expressions equal to each other:

[x + 30]° = [3x - 18]°

-[3x]° - [3x]°

___________

−18° = 30° - [2x]°

- 30° - 30°

____________

−48° = [−2x]°

____ ___

−2° −2°

`24° = x` [Plug this back into both expressions to get both m∠N and m∠M at 54°.]

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