Question

What is mBC


40
58
76
96

Answer 1

The correct option is C.

Explanation:

Given information: ∠A=20° and Arc(DE)=116°.

According to the Angle of Intersecting Secants Theorem:

If two lines intersect outside a circle, then the measure of an angle formed by the two lines is one half the difference of major arc and minor arc.

`\text{Angle between two lines}=(1)/(2)(\text{Major arc - Minor arc})`

`\angle A=(1)/(2)(Arc(DE)-Arc(BC))`

`20=(1)/(2)(116-Arc(BC))`

Multiply both sides by 2.

`40=116-Arc(BC)`

`Arc(BC)=116-40`

`Arc(BC)=76`

The measure of arc BC is 76°. Therefore the correct option is C.