Question

Look at quadrilateral LMJK in the circle shown below.



Based on this figure which statement proves that the opposite angles of an inscribed quadrilateral are supplementary?

Angle KJM is a, angle KLM is b, and a + b + angle JKL + angle LMJ = 360°.

Angle KLM is a, angle KJM is b, and a + b + angle JKL + angle LMJ = 360°.

a = 2 × angle KJM, b = 2 × angle KLM, and a + b = 360°.

a = 2 × angle KLM, b = 2 × angle KJM, and a + b = 360°.

Answer 1

@mathstudent55

Answer 2

@jim_thompson5910

Answer 3

are you familiar with the inscribed angle theorem

Answer 4

im familiar with it

Answer 5

can you see how this applies?

Answer 6

well ik that the quad is inscribed

Answer 7

honestly i have no idea...i did well on every section of geometry except for proofs

Answer 8

im awful

Answer 9

so each point of the quadrilateral is on the circle

Answer 10

that's what it means to be inscribed

Answer 11

understood

Answer 12

we know that arc KJM and arc KLM form a complete circle

Answer 13

so

arc KJM + arc KLM = 360

Answer 14

the value of 'a' is the measure of arc KLM and the value of b is the measure of arc KJM

so

arc KJM + arc KLM = 360

is really saying

b + a = 360

Answer 15

now this is where the inscribed angle theorem kicks in

angle KJM cuts off the arc KLM, so angle KJM is exactly half of angle KCM

ie angle KJM is exactly half of the value 'a'

so we can write this as

KJM = (1/2)*a

and solve for 'a' to get

a = 2*KJM

Answer 16

so C

Answer 17

yes

Answer 18

thx lol