Question

∠C and ​ ∠D ​ are vertical angles with m∠C=−3x+58 and m∠D=x−2 .

What is m∠D ?

Answer 1

vertical angles are equal

-3x + 58 = x - 2
-3x - x = -2 - 58
-4x = - 60
x = -60/-4
x = 15

m < D = x - 2....15 - 2 = 13 <====
m < C = -3x + 58....-3(15) + 58 = 13

Answer 2

m<D is
`13^(0)`

Explanation:

Vertically opposite angles are said to be equal angles, thus;

m<C = m<D

So that,

-3x + 58 = x -2

-3x - x = -2 -58

- 4x = - 60

x =
`(- 60)/(- 4)`

x = 15

Thus,

m< D = x - 2

= 15 - 2

=
`13^(0)`

Therefore, m<D is
`13^(0)`