What are the values of angles G and H?

G = 78°

H = 98°

Step-by-step explanation:

Opposite angles in a cylic quadrilateral are supplementary. Therefore:

G + E = 180°

Substitute

8x + 1 + 11x + 8 = 180°

Add like terms

19x + 9 = 180°

19x + 9 - 9 = 180° - 9

19x = 171

19x/19 = 171/19

x = 9

G = 8x + 1

Plug in the value

G = 8(9) + 1 = 73°

H + F = 180° (opposite angles of a cyclic quadrilateral is equal?

Plug in the values

6y - 4 + 5y - 3 = 180°

Add like terms

11y - 7 = 180

11y = 180 + 7

11y = 187

y = 187/11

y = 17

H = 6y - 4

Plug in the value of y

H = 6(17) - 4

H = 98°

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240