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2 years ago

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer.

Mathematics

1 answer:

AysviL [449]2 years ago

5 0

Answer:

< CFE = 40°

Step-by-step explanation:

To better understand the solution, see attachment for the diagram.

Given:

BC parallel to DE

Measure of Arc BD = 58°

Measure of Arc DE = 142°

First step: Draw a diameter that passes through the centre of the circle and name it. In this case, the diameter is line ST.

The line ST divides the arc BD and arc DE into half.

That is:

Arc SC = 1/2(arc BC) =1/2(58)

Arc SC = 29°

Arc TE = 1/2(arc DE) =1/2(142)

Arc TE = 71°

Arc SC + Arc CE + Arc TE = 180° (Sum of angles in a semicircle

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Inscribed angle = 1/2(intercepted angle)

<CFE = 1/2(Arc CE )

<CFE = 1/2(80)

< CFE = 40°

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<h3>Question: </h3><h3>In the diagram below of Δ ABC, side BC is extended to point D, m∠A = x , m∠B = 2x+15, and m∠ACD = 5x+5 , what is m∠B ?</h3>

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Since m∠C is supplementary to m∠ACD

m∠C = 180º - m∠ACD

m∠C = 180º -(5·x + 5)

m∠C = 180º -5 -5·x

m∠C = 175º - 5·x

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m∠A + m∠B + m∠C = 180º

x + 2·x + 15º + 175º - 5·x = 180º

3·x - 5·x +190º = 180º

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x = -10º/-2 = 5º

Now we can substitute this value of x in m∠B

m∠B = 2x+15

m∠B = 2·x + 15º = 2·5º + 15º = 10º + 15º = 25º

Answer: 3) m∠B = 25º

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