Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.

(BAC) B. 5x+4 at the top corner, A. 4x+14 at the bottom left, and C. 6x-3 on the right side

A. 59°, 63°, and 48°

B. 54°, 44°, and 82°

C. 59°, 58°, and 63°

D. 57°, 54°, and 69°

1 answer

To find the measure of the angles, we add up the measures of all three angles in the triangle and set it equal to 180°.

Given:
Angle BAC = 5x + 4
Angle ABC = 4x + 14
Angle ACB = 6x - 3

Adding up the measures and setting equal to 180°:
(5x + 4) + (4x + 14) + (6x - 3) = 180

Combining like terms:
15x + 15 = 180

Subtracting 15 from both sides:
15x = 165

Dividing both sides by 15:
x = 11

Now, plug x = 11 back into the original expressions for the angles to find their measures:
Angle BAC = 5x + 4 = 5(11) + 4 = 55 + 4 = 59°
Angle ABC = 4x + 14 = 4(11) + 14 = 44 + 14 = 58°
Angle ACB = 6x - 3 = 6(11) - 3 = 66 - 3 = 63°

Therefore, the measure of the angles for the triangle is:
A. 59°, 58°, and 63°