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

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.