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

Solution:

Given,

∠C and ∠D are vertical angles with m∠C = -x + 26 and m∠D = 2x - 10 .

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

This means

m∠C = m∠D.

Substituting in the equation, we get,

-x + 26 = 2x - 10.

Subtract 2x from both sides,

-3x + 26 = -10.

Subtract 26 from both sides,

-3x = -36

x = 12.

m∠D = 2x - 10.

m∠D = 2(12) - 10.

m∠D = 24 - 10

m∠D = 14.

Therefore, m∠D = 14.

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

Summary:

∠C and ∠D are vertical angles with m∠C = -x + 26 and m∠D = 2x - 10. m∠D = 14.