Question

What is mBC


40
58
76
96

Answer 1

Answer:

The correct option is C.

Step-by-step 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.

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

$\angle A=\frac{1}{2}(Arc(DE)-Arc(BC))$

$20=\frac{1}{2}(116-Arc(BC))$

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.