Question

The angles are a triangle are as follows: 2x, 3x, and 5x. Use the Triangle Angle Sum Theorem to determine the measure of each angle.


*Remember the sum of all the angles inside a triangle must equal 180 degrees.

A.
20, 30, 50

B.
32, 52, 96

C.
36, 54, 90

D.
40, 60, 80

Answer 1

To determine the measures of the angles in the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle equals 180 degrees.

Given the angles are \(2x\), \(3x\), and \(5x\), we can set up the following equation:

\[
2x + 3x + 5x = 180
\]

Combining like terms gives us:

\[
10x = 180
\]

Next, we solve for \(x\):

\[
x = \frac{180}{10} = 18
\]

Now, we can find the measure of each angle:

1. \(2x = 2 \times 18 = 36\)
2. \(3x = 3 \times 18 = 54\)
3. \(5x = 5 \times 18 = 90\)

Thus, the measures of the angles are \(36\), \(54\), and \(90\) degrees.

The answer corresponds to option:

**C. 36, 54, 90**