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 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

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°

The answer is going to be B.40

2.  40^{circ}

Step-by-step explanation:

Given : In the diagram, overline{AC} is a diameter of the circle with center O.

mangle{ACB}=50^{circ}

We know that the angle subtended by the diameter to the circumference is equal to 90^{circ}

Using angle sum property of triangles in  triangle{AOB}, we get

angle{BAC}+angle{ABC}+angle{ACB}=180^{circ}\\Rightarrowangle{BOC}+50^{circ}+90^{circ}=180^{circ}\\Rightarrowangle{BOC}+140^{circ}=180^{circ}\\Rightarrowangle{BOC}=180^{circ}-140^{circ}=40^{circ}

Hence, mangle{BAC}=40^{circ}

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°

The answer is going to be 40

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