Angle C and angle D are vertical angles with m angle C = -x + 26 and m angle D = 2x - 10. What is m angle D?

m∠D = 14

Step-by-step explanation:

According to the vertical angle theorem, both of these angles are congruent.

This means that they are equal (m∠C = m∠D) and we can solve for x:

m∠C = m∠D

-x + 26 = 2x - 10 (substitute in the equations)

-3x + 26 = -10 (subtract 2x from both sides)

-3x = -36 (subtract 26 from both sides)

x = 12 (divide both sides by -3)

Now that we know what x is, we can find m∠D by plugging it back into the equation:

m∠D = 2x - 10

m∠D = 2(12) - 10 (substitute the value for x in)

m∠D = 24 - 10

m∠D = 14

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