Final answer:
To solve for m∠D, we set the expressions for m∠C and m∠D equal because they are vertical angles. After solving for x, we found m∠D to be 14 degrees, which is not listed in the available options, indicating a potential error in the question. Any of the given choices A) x - 16, B) 2x - 10, C) 26 - x, or D) x + 16.
Step-by-step explanation:
To determine the measure of ∠D, we need to use the fact that ∠C and ∠D are vertical angles, which means they are equal. Given that m∠C = -x + 26 and m∠D = 2x - 10, we can set these two expressions equal to each other because vertical angles have equal measures.
Setting the expressions equal, we get:
-x + 26 = 2x - 10.
Now, we solve for x:
Add x to both sides: 26 = 3x - 10.
Add 10 to both sides: 36 = 3x.
Divide both sides by 3: x = 12.
To find m∠D, we substitute x into the given expression for m∠D:
m∠D = 2x - 10 = 2(12) - 10 = 24 - 10 = 14.
Therefore, the measure of ∠D is 14 degrees, which is not present in the provided options. There appears to be a mistake in the options given. m∠D should be 14 degrees, rather than any of the given choices A) x - 16, B) 2x - 10, C) 26 - x, or D) x + 16.