Final answer:
The measure of angle D is -26 degrees, which is equal to the measure of angle C, as they are vertical angles.
Step-by-step explanation:
The measure of vertical angles are equal. Given that m∠C = -26° and m∠D = 2x - 10°, we can set them equal to each other since they are vertical angles:Vertical angles are formed when two lines or rays intersect, and they have equal measures. In this case, ∠C and ∠D are vertical angles. Given that m∠C = -26°, we can use this information to find the measure of ∠D. It is given that m∠C = -26°, and we can find m∠D using the equation m∠D = 2x - 10°. We can substitute -26° for m∠C and solve for x.
So, -26° = 2x - 10°Adding 10° to both sides: -26° + 10° = 2xCombining like terms: -16° = 2xDividing by 2: x = -8°Now that we have the value of x, we can substitute it back into the equation m∠D = 2x - 10° to find the measure of ∠Dm∠D = 2(-8°) - 10° = -16° - 10° = -26°Therefore, the measure of ∠D is -26°. So, the correct answer is d. -26°-26° = 2x - 10To solve for x, we will add 10° to both sides:-26° + 10° = 2x-16° = 2xNext, divide both sides by 2 to solve for x:-8° = xNow, plug the value of x back into the expression for m∠D:m∠D = 2(-8°) - 10°m∠D = -16° - 10°m∠D = -26°The measure of angle D is -26°, which corresponds to option (d).