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Andru [333]
2 years ago
14

Solve this problem, which steps would you take? Include any theorems, definitions, or reasons that explain the steps. Make sure

you include all steps needed to solve for ∠A

Mathematics
1 answer:
posledela2 years ago
6 0

Answer:

∠A=123°.

Step-by-step explanation:

From the given figure it is clear the CD and CE are two tangent lines on circle with center A.

Radius is perpendicular to the tangent at the point of tangency.

\angle ADC=90^{\circ}

\angle AEC=90^{\circ}

Smaller arc DE = (5x-2)°

It means central angle DAE is (5x-2)°.

\angle DAE=(5x-2)^{\circ}

Now, ADCE is a quadrilateral and sum of all angles of a quadrilateral is 360 degrees.

\angle ADC+\angle DCE+\angle AEC+\angle DAE=360^{\circ}

90^{\circ}+(2x+7)^{\circ}+90^{\circ}+(5x-2)^{\circ}=360^{\circ}

(7x+5)^{\circ}+180^{\circ}=360^{\circ}

(7x+5)^{\circ}=360^{\circ}-180^{\circ}

(7x+5)^{\circ}=180^{\circ}

7x+5=180

7x=175

x=25

The value of x is 25.

\angle A=5x-2=5(25)-2=125-2=123^{\circ}

Therefore, the measure of ∠A is 123°.

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