Answer:
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
