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.

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°

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

42

step-by-step explanation: