Choose the one alternative that best completes the statement or answers the question. Solve the problem.
-The sum of the measures of the angles in any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while angle C is 114 degrees larger than each of the other two angles. Find the measure of angle C.
A) 22 degrees
B) 44 degrees
C) 136 degrees
D) 158 degrees

Question

Quizplus · Accepted Answer

Since the sum of the angles in a triangle is 180 degrees and angle C is 114 degrees larger than each of the other two angles (which are equal), we can set up the equation: A + B + C = 180. Given A = B and C = A + 114, we can substitute to get 2A + (A + 114) = 180, simplifying to 3A + 114 = 180. Solving for A gives A = 22, so C = 22 + 114 = 136 degrees.

Choose the One Alternative That Best Completes the Statement or Answers