Question

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

Answers are 
1.50
2.40
3.80
4.100

Answer 1

Answer: 2.
`40^(\circ)`

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)`

Answer 2

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°