Question

Given:Circle B with tangent AD and tangent DC. Arc AC has a measure of 85. What is the relationship between m

Answer 1

They are supplementary

Step-by-step explanation:

If AD is tangent to circle B, then the measure of ∠BAD is 90°. In the same way, if DC is tangent to circle B, the measure of ∠DCB is 90°.

So, we can complete the graph as:

Then, the sum of the interior angles of a quadrilateral is 360°, so we can calculate the m∠ADC as:

m∠ADC = 360 - 90 - 90 - 85

m∠ADC = 95°

Now, the sum of m∠ABC and m∠ADC is equal to:

m∠ABC + m∠ADC = 85 + 95 =180

Since the sum is 180, we can say that ∠ABC and ∠ADC are supplementary angles.