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°
15°, 75°, and 90°

Answer 1

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

\[ 2x + 4x + 6x = 12x \] So the equation now reads:

\[ 12x = 180° \]

Now, we can solve for \(x\) by dividing both sides of the equation by 12:

\[ x = \frac{180°}{12} = 15° \]

Next, we can find the measures of the angles by substituting \(x\) back into each expression for the angles:

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

Therefore, the measures of the angles in the triangle are 30°, 60°, and 90°.

So, the correct response is:

30°, 60°, and 90°