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°

idk the answer but just put a

step-by-step explanation:

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.