Question

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°

Answer 1

Answer;

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°

Answer 2

The solution of  m∠BAC is mathematically given as

m∠BAC = 40°. This is further explained below.

What is angle

The angle formed by two crossing lines or surfaces, commonly expressed as a number of degrees.

What is the solution of  m∠BAC?

Generally, the equation for angle m∠BAC  is mathematically given as

m∠BAC = 180 - (m∠ACB + m∠ABC)

m∠BAC = 180 - (50 + 90)

m∠BAC = 40°

In conclusion, m∠BAC = 40°

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