Question

One angle of a triangle has a measure of 66°. the measure of the third angle of 57° more than 1/2 the measure of the second angle. the sum of the angle measures of a triangle is 180°. what is the measure of the second angle

Answer 1

Refer to the figure shown below.

Let x =  measure of the second angle.

The measure of the third angle is 57° more than 1/2 the measure of the second angle. Therefore the measure of the third angle is x/2 + 57°.

The sum of the angles in a triangle is 180°. Therefore

66 + x + (x/2 + 57) = 180
(3/2)x + 123 = 180
(3/2)x = 57
x = (2/3)*57 = 38°

Answer: The measure of the second angle is 38°