Question

What is the measure of arc ADC if the measure of arc BC is 52 degrees

Answer 1

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Answer 2

The measure of arc ADC is 128 degrees.

Step-by-step explanation:

The relationship between arcs in a circle states that the sum of the measures of complementary arcs is 180 degrees. If the measure of arc BC is 52 degrees, then the measure of its complement, arc ADC, can be found by subtracting the measure of arc BC from 180 degrees.

`\[ \text{Arc ADC} = 180^\circ - \text{Arc BC} \]`

`\[ \text{Arc ADC} = 180^\circ - 52^\circ = 128^\circ \]`

Therefore, the measure of arc ADC is 128 degrees. This calculation is based on the concept that in a circle, the sum of complementary arcs is always 180 degrees. In this case, we subtract the given measure of arc BC from 180 to find the measure of arc ADC.