Question

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

Answer 1

So we have to find out what x is before we can solve for either angle

because vertical angles are always congruent we can set the two equations to equal each other and solve for x

so

-3x + 58 = x - 2

we need to get all the x terms on one side before we can solve for x so let's add 2 to both sides to get x alone on the right side

now we have

-3x + 60 = x

now we add 3x to both sides

60 = 4x

we isolated the terms and now we can solve for x by dividing both sides by 4

15 = x

so if x = 15 we need to plug that in to both equations to check our work

C = -3(15) + 58

C = 13

D = 15 - 2

D = 13

x does in fact equal 15 because both equations got the same answer and we found out that angle D = 13