Question

A convex pentagon has the following measurements for its interior angles: (x-8), (3x-11), (x+8), (x), and (2x+7). Which of the following could be measurements for interior angles of the pentagon? Select all that apply.
A: 60



B: 68



C: 76



D: 108



E: 193



F: 540

Answer 1

The correct answer isthe sum of all the internal angles of a convex pentagon is 540. Also, if the pentagon is regular, each of its internal angles measures 108 degrees. Therefore, the correct answers for this case would be:The value of x can be found as the sum: x + (x + 8) + (3x-11) + (x-8) + (2x + 7) = 540 resulting in x = 68.Then, (68 + 8) = 76; (3 * 68-11) = 193; (68-8) = 60; (2 * 68 + 7) = 143 and (x) = 68The correct answers are: B: 68, E: 193, C: 76, A: 60.