Question

Given: DR tangent to Circle O.
If m _ RDC = 120°, then m DAC =
•60
•120
•240

Answer 1

Option C.

Explanation:

If a tangent and arc intersect at a point on a circle the measure of angle formed by the intersection will be half of the arc intercepted.

Therefore, m∠RDC =
`(1)/(2)(mDAC)`

Since m∠RDC = 120°

120 =
`(1)/(2)(mDAC)`

m(arcDAC) = 2×120°

m(arcDAC) = 240°

Option C. 240° is the answer.

Answer 2

The measure of the arc DAC is 240°

Explanation:

we know that

The semi-inscribed angle is half that of the arc it comprises.

so

m∠RDC=(1/2)[arc DAC]

we have

m∠RDC=120°

substitute

120°=(1/2)[arc DAC]

240°=[arc DAC]

Rewrite

arc DAC=240°