Question

select the correct answer.
in the diagram, (overline{ac}) is a diameter of the circle with center (o). if (mangle acb = 50^circ), what is (mangle bac)?
a. (50^circ)
b. (40^circ)
c. (80^circ)
d. (100^circ)

Explanation:

Step1: Identify right angle at B

Since $\overline{AC}$ is a diameter, $\angle ABC = 90^\circ$ (Thales' theorem).

Step2: Sum of triangle angles is $180^\circ$

Let $m\angle BAC = x$. Use $\angle ABC + \angle ACB + \angle BAC = 180^\circ$
$\implies 90^\circ + 50^\circ + x = 180^\circ$

Step3: Solve for $x$

$x = 180^\circ - 90^\circ - 50^\circ = 40^\circ$

Answer:

B. $40^\circ$