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In the circle shown, secants PE and PF have been drawn such that arc CE = 82, arc DF=98 and the ratio of arc CD to arc EF is 2:7. Determine the measure of angle P. Show how you arrived at your answer.

In the circle shown secants PE and PF have been drawn such that arc CE 82 arc DF98 and the ratio of arc CD to arc EF is 27 Determine the measure of angle P Show class=

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Answer:

m<P = 50°

Step-by-step explanation:

Given:

Arc CE = 82°

Arc DF = 98°

Ratio of arc CD to Arc EF = 2:7

Thus, let,

Arc CD = 2x

Arc EF = 7x

A full circle = 360°

Therefore,

Arc CE + Arc DF + Arc CD + Arc EF = 360°

Substitute

82° + 98° + 2x + 7x = 360°

Add like terms

180° + 9x = 360°

Subtract 180° from both sides

180° + 9x - 180° = 360° - 180°

9x = 180°

Divide both sides by 9

9x/9 = 180/9

x = 20

✔️Arc CD = 2x

Plug in the value of x

Arc CD = 2(20) = 40°

Arc EF = 7x = 7(20) = 140°

✔️Find m<P:

Recall: the measure of the external angle created when two secants intersect = half the difference of the major and minor arcs that are intercepted

Thus:

m<P = ½(arc EF - arc CD)

Substitute

m<P = ½(140° - 40°)

m<P = ½(100°)

m<P = 50°

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