Questions: Circle Relationships: Mastery Test Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). In this figure, m angle BDA= - and m angle BCA= :

Circle Relationships: Mastery Test

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

In this figure, m angle BDA= - and m angle BCA= :
Transcript text: Circle Relationships: Mastery Test Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). In this figure, m $\angle B D A=$ $\square$ - and $\mathrm{m} \angle B C A=$ $\square$ :
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Solution

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Solution Steps

Step 1: Find the measure of angle BDA

The measure of an inscribed angle is half the measure of its intercepted arc. Angle BDA intercepts arc AB, which has a measure of 29°. Therefore, the measure of angle BDA is 29/2 = 14.5°.

Step 2: Find the measure of angle BCA

The lines BC and AC are tangent to the circle. The measure of the angle formed by the two tangents is half the difference of the intercepted arcs. Angle BCA intercepts arcs AB and ADB. Arc ADB is 360 - 29 = 331 degrees. So, the measure of angle BCA is (331-29)/2 = 302/2 = 151°.

Final Answer:

m∠BDA = 14.5° and m∠BCA = 151°

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