Question

Find the measure of

Answer 1

20°

Explanation:

In circle geometry, one of the theorem States that angle at the center of a circle is twice angle at the circumference.

Let x be the angle at the centre and y be angle at the circumference. The theorem can be expressed mathematically as;

x = 2y

According to the diagram <BOC is the angle at the center represented as x which is 40°

Angle<BAC is at the circumference of the circle represented as y.

To find <BAC, note that

<BOC = 2<BAC

40° = 2<BAC

<BAC = 40°/2

<BAC = 20°

Answer 2

The measure of angle BAC is 20°

Explanation:

step 1

Find the measure of arc BC

we have that

m∠BOC=arc BC ------> by central angle

we have

m∠BOC=40°

therefore

arc BC=40°

step 2

Find the measure of angle BAC

we know that

The inscribed angle is half that of the arc it comprises

so

m∠BAC=(1/2)[arc BC]

we have

arc BC=40°

substitute

m∠BAC=(1/2)[40°] =20°