Question

Question

Based on Triangle Angle Sum Theorem, the sum of the angles inside a triangle must equal 180°.

Use the equation 2x + 4x + 6x = 180° to solve the measures of the angles in this triangle.

(2 points)
Responses

30°, 30°, and 120°
30°, 30°, and 120°

15°, 60°, and 105°
15°, 60°, and 105°

30°, 60°, and 90°
30°, 60°, and 90°

15°, 75°, and 90°

Answer 1

To solve the equation \(2x + 4x + 6x = 180°\), we first combine like terms:

\[ 2x + 4x + 6x = 12x \]

So the equation becomes:

\[ 12x = 180° \]

Next, we divide both sides by 12:

\[ x = \frac{180°}{12} = 15° \]

Now we can find the measures of the angles:

1. The first angle: \(2x = 2(15°) = 30°\)
2. The second angle: \(4x = 4(15°) = 60°\)
3. The third angle: \(6x = 6(15°) = 90°\)

Thus, the measures of the angles in the triangle are:

\[ 30°, 60°, \text{ and } 90° \]

So the correct response is:

30°, 60°, and 90°