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nata0808 [166]
3 years ago
8

If the measure of angle def is 65° what is the measure of arc de?

Mathematics
1 answer:
Vladimir79 [104]3 years ago
3 0

EF is tangent to the circle we'll assume; otherwise there's no progress.

Call the center C. ECD is isosceles, formed from two radii and the chord.

Angle CED is complementary to DEF

CED = 90 - 65 = 25 degrees

CDE is congruent, isosceles triangle and all that: CDE=25

That leaves DCE=180-25-25=130 degrees

That's the measure of arc DE as well:

Answer: 130 degrees, choice A

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