Question

If AC is a diameter and Arc AD = 90. Find ∠DAC. Round your answer to the nearest tenth.

Answer 1

45°

Step-by-step explanation:

it is an inverted angle within a circle

Answer 2

Answer: 45 degrees

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Step-by-step explanation:

Minor arc AD is the shortest path from A to D along the circle's edge. This is 90 degrees. Minor arc AD combines with DC to get arc ADC

Arc ADC is a semicircle because of the diameter AC. Any semicircle has a measure of 180 degrees.

So,

(minor arc AD) + (minor arc DC) = arc ADC

(minor arc AD) + (minor arc DC) = 180

(90) + (minor arc DC) = 180

minor arc DC = 180 - 90

minor arc DC = 90

AD and DC are 90 degrees each.

Then notice that inscribed angle DAC subtends minor arc DC. Use the inscribed angle theorem to determine angle DAC is 90/2 = 45 degrees