Given: klij is inscribed in circle k(o)
m∠k = (9x+1)°,
m (arc) li = (10x−1)°
m (arc) ij = 59°,
m (arc) kj =97°
find: all angles of klij

Check the picture below.

let's notice that the angle at K is an inscribed angle with an intercepted arc

now, let's notice something again, the angle at L is also an inscribed angle, intercepting and arc of 97 + 59 = 156, so then, by the inscribed angle theorem,

∡L is half that, or 78°.

now, let's take a look at the picture down below, to the inscribed quadrilateral conjecture, since ∡J and ∡I are both supplementary angles, then

∡I = 180 - 64 = 116°.

∡J = 180 - 78 = 102°.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

may i see the picture? it would a lot, xox