In the diagram, ac is a diameter of the circle with center o. if m∠acb = 50°, solve for m∠bac. a. 50° b. 40° c. 80° d. 100°

### Answers

B. 40°

m∠BAC = 40°

Explanation;In the question AC is the diameter of the circle. ACB is a triangle with angles m∠BAC, m∠ACB and m∠ABC.Angles subtended by a diameter to the circumference of a circle is always right angle or 90 degrees.Therefore, angle m∠ABC, which is subtended by diameter AC to the circumference is 90 degrees.

But, angles in a triangle adds up to 180 degrees, therefore;

m∠BAC = 180 - (m∠ACB + m∠ABC)

= 180 - (50 + 90)

= 180 - 140

= 40°

Thus; m∠BAC = 40°

2.

Step-by-step explanation:

Given : In the diagram, is a diameter of the circle with center O.

We know that the angle subtended by the diameter to the circumference is equal to

Using angle sum property of triangles in , we get

Hence,

Answer

2. 40

Explanation

The angle subtended by the diameter to the circumference is equal to 90°.

∴ angle ABC = 90°

Angles in a triangle = 180°

50 + 90 + x = 180

90 + x = 180

x = 180 - 90

= 90°