1. In circle o, chord AB and tangent CAD are drawn. It is known that mAB=116 . Find each of the
following:
(a) the measure of BEA
(b) the measure of ZCAB

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°

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step-by-step explanation:

2/5+1/2=9/10

6/1-9/10=5 1/10

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

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