Question

Angle A is circumscribed about circle O.
What is the measure of D?

Answer 1

50

Explanation:

Answer 2

m<D=50

Explanation:

The reason is that ABOC is a quadrilateral, so its angle add up to 360*. Each of the tangent angles, <ABO and <ACO, has a measure of 90*.

m<ABO + m<ACO + m<A + m<O = 360

90 + 90 + m<A + m<O = 360

m<A + m<O = 180

80 + m<O =180

m<O = 100

If the measure of central angle <O is 100*, what is the measure of inscribed <D?

The measure of a central angle is equal to the measure of the arc it intercepts. If m<O = 100*, then m BC = 100.

The measure of an inscribed angle is half of the measure of the arc it intercepts. If m BC = 100*, then m<D = 50

m<D=50