The sum of the measures of the angles of any triangle is $180^{\circ}$. In triangle $A B C$, angles $A$ and $B$ have the same measure, while the measure of angle $\mathrm{C}$ is $60^{\circ}$ larger than each of $\mathrm{A}$ and $\mathrm{B}$. What are the measures of the three angles?
A) A and B: $100^{\circ}$; C: $40^{\circ}$
B) A and B: $50^{\circ}$; C: $80^{\circ}$
C) A and C: $80^{\circ}$; B: $50^{\circ}$
D) A and B: $40^{\circ}$; C: $100^{\circ}$

Question

Quizplus · Accepted Answer

Since angles A and B are equal and angle C is 60° larger than each of A and B, let's denote the measure of angles A and B as x. Therefore, the measure of angle C is x + 60°. The sum of the angles in a triangle is 180°, so we have the equation: x + x + (x + 60°) = 180°. Simplifying this gives 3x + 60° = 180°, and solving for x gives x = 40°. Therefore, angles A and B are 40° each, and angle C is 100°.

The Sum of the Measures of the Angles of Any 180∘180^{\circ}180∘

The Sum of the Measures of the Angles of Any $180^{\circ}$