Question

∠C and ​ ∠D ​ are vertical angles with m∠C=−2x+90 and m∠D=x−30 . What is m∠D ?

Answer 1

∠C = ∠ D (vertical angles

C= -2x + 90
D= x-30

Since C = D , Then -2x + 90 = x-30

-2x - x = - 30 - 90

-3x = -120

3x = 120 and x = 40°. Now replace x by 40 in any of the equality, say :
D = x-30 ; D = 40 - 30 and D = 10°

Answer 2

The measure of m∠D is 10 degrees

In line geometry, vertical angles are always equal.

Given the following vertical angles

m∠C=−2x+90 and m∠D=x−30

Since m∠C= m∠, hence;

-2x + 90 = x - 30

-2x - x = -30 - 90

-3x = -120

x = 40

Get the measure of m∠D

m∠D = x - 30

m∠D = 40 - 30

m∠D = 10degree

Hence the measure of m∠D is 10 degrees

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