Use the triangle angle su theorem to find the measure of the angles for the triangle in the diagram.

Question

Angle A : 4x + 14

Angle B : 5x + 4

Angle C : 6x - 3

A. 54, 44, and 82

B. 59, 58, and 63

C. 57, 58, and 63

D. 59, 63, and 48

Answer 1

To use the triangle angle sum theorem, we know that the sum of all angles in a triangle is 180 degrees. Therefore, we can set up the equation:

4x + 14 + 5x + 4 + 6x - 3 = 180

Combine like terms:

15x + 15 = 180

Subtract 15 from both sides:

15x = 165

Divide both sides by 15:

x = 11

Now, we can substitute x = 11 back into the expressions for each angle:

Angle A = 4(11) + 14 = 48 + 14 = 62 degrees
Angle B = 5(11) + 4 = 55 + 4 = 59 degrees
Angle C = 6(11) - 3 = 66 - 3 = 63 degrees

Therefore, the measure of the angles for the triangle is 62 degrees, 59 degrees, and 63 degrees.

The answer is D. 59, 63, and 48.