Everyday, Sarah drives the same distance to work and back home. If Sarah drove 1,005 miles in 5 days , how far did Sarah drive 3
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Given:
m(ar AB) = 116°
To find:
1. The measure of arc BEA.
2. The measure of ∠CAB
3. The measure of ∠BAD
Solution:
1. The measure of arc of full circle is 360°.
m(ar AB) + m(ar BEA) = 360°
116° + m(ar BEA) = 360°
Subtract 116° from both sides.
m(ar BEA) = 244°
2. Using the tangent-chord angle theorem:
⇒ m∠CAB = 58°
3. Using the tangent-chord angle theorem:
⇒ m∠BAD = 122°
Using the fact that it is supplementary to ∠CAB.
⇒ m∠CAB + m∠BAD = 180°
⇒ 58° + m∠BAD = 180°
Subtract 58° from both sides.
⇒ m∠BAD = 122°