Question

In the diagram, `bar(AC)` is a diameter of the circle with center O. If m`/_ACB` = 50°, what is m`/_BAC`?

Answer 1

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°

Answer 2

Answer: 2.  $40^{\circ}$

Step-by-step explanation:

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

$m\angle{ACB}=50^{\circ}$

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

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

Hence, $m\angle{BAC}=40^{\circ}$