Question

In triangle ABC, if AC = CB, and MZA = 3x + 18, m_B = 7x - 58, what is the value of angle MZA?

A. 48 degrees
B. 60 degrees
C. 75 degrees
D. 90 degrees

Answer 1

Angle MZA can be found by setting the expressions for the isosceles triangle's equal angles, solving for x, and substituting x back into the expression for mZA. The value of angle MZA is 75 degrees.

Step-by-step explanation:

To solve for the value of angle MZA in triangle ABC where AC = CB and mZA = 3x + 18, mB = 7x - 58, we must recognize that AC = CB indicates that triangle ABC is isosceles, with angles ZA and B being equal. Setting the expressions for these equal angles gives us the equation 3x + 18 = 7x - 58. Solving for x yields:

3x + 18 = 7x - 58

• 4x = 76
• x = 19

Substituting x back into the expression for mZA gives:

• mZA = 3(19) + 18
• mZA = 57 + 18
• mZA = 75 degrees

Therefore, the correct answer is C. 75 degrees.