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Sagot :
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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