Given: m arc kj = 124°, m arc ic =38° find: m∠cqj, m∠lij.

Part 1) The measure of angle LIJ is

Part 2) The measure of angle CQJ is

Step-by-step explanation:

step 1

Find the measure of angle KIJ

we know that

The inscribed angle measures half that of the arc comprising

so

substitute

step 2

Find the measure of angle LIJ

we know that

-----> by supplementary angles

substitute

step 3  

Find the measure of angle IKQ

we know that

The inscribed angle measures half that of the arc comprising

so

step 4

Find the measure of angle IQK

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

In the triangle IQK

substitute the values

step 5

Find the measure of angle CQJ

we know that

m<CQJ=m<IQK -----> by vertical angles

so

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x