Question

In AABC, if AC CB, mZA= (3x + 18). m/B= (7x-58), and m/C= (2x-8), find the value

of x and the measure of each angle.

Answer 1

In triangle ABC, the value of x is 19. Angle A measures 75 degrees, Angle B measures 45 degrees, and Angle C measures 30 degrees.

Step-by-step explanation:

In triangle ABC, if AC = CB, then triangle ABC is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, angle A is equal to angle C.

To find the value of x and the measure of each angle, set up an equation:

3x + 18 + 7x - 58 + 2x - 8 = 180

Combine like terms:

12x - 48 = 180

Add 48 to both sides of the equation:

12x = 228

Divide both sides by 12:

x = 19

To find the measure of each angle:

Angle A = 3x + 18 = 3(19) + 18 = 75 degrees

Angle B = 7x - 58 = 7(19) - 58 = 45 degrees

Angle C = 2x - 8 = 2(19) - 8 = 30 degrees

Learn more about Triangle angles