Question

A triangle has 3 angles that measure (X-30), (2X-120), and (1/2+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

The angles in the triangle, given by the expressions (X-30), (2X-120), and (1/2X+15), are solved by setting up the equation X - 30 + 2X - 120 + 1/2X + 15 = 180. Solving for X gives 90 degrees, which determines each angle to be 60 degrees. Therefore, the triangle is equilateral with angles 60, 60, 60.

Step-by-step explanation:

The subject of the question is Mathematics, specifically, it involves solving for the angles of a triangle. We know that the sum of the angles in a triangle is always 180 degrees. The triangle in the question has angles with expressions (X-30), (2X-120), and (1/2X+15). To find the actual angle measures, we can set up the equation:

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

Combining like terms gives us:

3.5X - 135 = 180.

Add 135 to both sides gives us:

3.5X = 315.

Dividing both sides by 3.5 gives us:

X = 90.

Now, we can find the measures of each angle:

• (X - 30) = (90 - 30) = 60 degrees,
• (2X - 120) = (2*90 - 120) = 60 degrees,
• (1/2X + 15) = (1/2*90 + 15) = 60 degrees.

All three angles are 60 degrees, indicating that the triangle is equilateral. The answer is therefore (b) 60, 60, 60.