Answer:
∠A = 64°
Explanation:
You have a triangle inscribed in a semicircle with acute angles marked A=(5x-1)° and C=(2x)°.
Right triangle
A triangle inscribed in a semicircle is a right triangle. (You know that because angle B is half the measure of 180° arc AC.) That means the two marked angles total 90°:
(5x -1) +(2x) = 90
7x = 91
x = 13
Then angle A is ...
A = (5·13 -1)° = (65 -1)° = 64°
The measure of angle A is 64°.
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Check:
C = (2x)° = (2·13)° = 26°
Then A+C = 64° +26° = 90°, as required.