Question

Inscribed angles math lib Need help with 9 and 10 thank you!!

Answer 1

Answer:

54° and 110°

Step-by-step explanation:

The opposite angles of a cyclic quadrilateral are supplementary, sum to 180°

(9)

19x - 26 + 7x - 2 = 180

26x - 28 = 180 ( add 28 to both sides )

26x = 208 ( divide both sides by 26 )

x = 8

Then

∠ EFG = 7x - 2 = 7(8) - 2 = 56 - 2 = 54°

(10)

21x - 33 + 14x + 3 = 180

35x - 30 = 180 ( add 30 to both sides )

35x = 210 ( divide both sides by 35 )

x = 6

Then

∠ YVW = 14x + 3 = 14(6) + 3 = 84 + 3 = 87°

The inscribed angle YVW is half the measure of its intercepted arc YW, so

arc YW = 2 × 87° = 174°, then

arc XW = 174° - 64° = 110°