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

In the diagram, AC is the diameter of the circle centered at O. If the measure of angle ACB is 50°, what is the measure of angle BAC?

a. 50°
b. 40°
c. 80°
d. 100°

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5 Answers

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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°
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Anonymous

Feb 16, 2025

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 getHence,
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A
Anonymous

Feb 03, 2025

Answer2. 40ExplanationThe angle subtended by the diameter to the circumference is equal to 90°. ∴ angle ABC = 90°   Angles in a triangle = 180°   50 + 90 + x = 18090 + x = 180x = 180 - 90  = 90°
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Geometry Angles Circles

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