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°

the answer is a

step-by-step explanation:

because your just changing the position of where the shape is

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°