Question

A triangle has three angles that measure X-30, 2X-120, and 1/2 X+15. What are the angle measures?

a) 120, 30, 30
b) 60, 60, 60
c) 30, 60, 90
d) 50, 70, 60
e) 45, 45, 90

Answer 1

To find the angle measures of the triangle, we can solve the equation by combining like terms and simplifying. The angle measures of the triangle are 96°, 132°, and 78°. Answer choice (d) 50, 70, 60 is the closest to the correct answer.

Step-by-step explanation:

To find the angle measures of the triangle, we need to solve the equation:

X-30 + 2X-120 + 1/2 X+15 = 180

Simplifying the equation, we get:

2.5X - 135 = 180

Adding 135 to both sides, we get:

2.5X = 315

Dividing both sides by 2.5, we get:

X = 126

Substituting the value of X back into the angle measures, we get:

X-30 = 126-30 = 96

2X-120 = 2(126)-120 = 252-120 = 132

1/2 X+15 = 1/2(126)+15 = 63+15 = 78

Therefore, the angle measures of the triangle are 96°, 132°, and 78°. Answer choice (d) 50, 70, 60 is the closest to the correct answer.