Final answer:
To find the measure of angle a in triangle ABC with congruent angles a and c and with angle b measuring 93.5°, solve 2a + 93.5° = 180° to obtain a = 43.25°.
Step-by-step explanation:
The question requires finding the measure of ∠a in a triangle ABC where angles a and c are congruent, and angle b measures 93.5°. Since the sum of angles in any triangle is 180 degrees, we can set up an equation to find the measure of the congruent angles a and c.
The equation is: a + a + 93.5° = 180°. This simplifies to 2a + 93.5° = 180°, and by subtracting 93.5° from both sides, we get 2a = 86.5°. Dividing by 2, we find that a = 43.25°.