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Given:circle O, with tangent segments AC and AB . What is the measure of angle A

Givencircle O With Tangent Segments AC And AB What Is The Measure Of Angle A class=

Sagot :

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Answer:

B 84

Step-by-step explanation:

Angle COB = 96 (Angle CDB x2)

Lets split Quadrileteral ABOC into 2 equal parts.

Angle ABO = 90 (tangent segment of circle)

Angle AOB = 96/2 = 48

Angle OAB = 180 - 90 - 48 = 42

Angle A = Angle OAB x 2 = 42 x 2 = 84

Therefore Answer is B.

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The measure of angle A in the given cyclic quadrilateral is determined as 84⁰.

Measure of angle A

The measure of angle A is determined from the following steps;

Determine angle COB

∠COB = 96 (angle at center is twice angle at the circumference)

Consider the following triangles;

Δ AOB + Δ AOC = COB

Determine angle AOB

∠ABO = 90 (tangent segment of circle)

∠ AOB = 96/2 = 48

Determine angle OAB

∠OAB = 180 - 90 - 48 = 42

Since, angle OAB is half of angle A in the quadrilateral OCAB

Angle A = ∠OAB x 2 = 42 x 2 = 84⁰

Thus, the measure of angle A in the given cyclic quadrilateral is determined as 84⁰.

Learn more about cyclic quadrilateral here: https://brainly.com/question/10057464

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