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°
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
Thus; m∠BAC = 40°
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
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