Question

HELP!! pls this is the last chance

Answer 1

Explanation:

the arc angle KLI = 142°.

that means that the arc angle KJI = 360 - 142 = 218°.

this is twice the inscribed opposite angle on the arc (L).

so,

(a)

angle KLI = 218/2 = 109°

(b)

for the same reason

angle LKJ is half of the arc angle LIJ.

arc angle LIJ = 2× angle LKJ = 2×66 = 132°

that means

arc angle LKJ = 360 - 132 = 228°

angle LIJ = half of arc angle LKH = 228/2 = 114°

FYI for such an inscribed quadrilateral there is Akari the rule that the sum of opposite angles have to be 180°.

so, angle LIJ is opposite of angle LKJ.

angle LIJ = 180 - angle LKJ = 180 - 66 = 114°