Question

Given: m arc KJ = 124°, m arc IC =38° Find: m∠CQJ, m∠LIJ.

Answer 1

Answer:

Part 1) The measure of angle LIJ is $m$

Part 2) The measure of angle CQJ is $m$

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

$m$

substitute

$m$

step 2

Find the measure of angle LIJ

we know that

$m$ -----> by supplementary angles

substitute

$m$

$m$

step 3  

Find the measure of angle IKQ

we know that

The inscribed angle measures half that of the arc comprising

so

$m$

$m$

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

$m$

substitute the values

$19\°+62\°+m$

$m$

step 5

Find the measure of angle CQJ

we know that

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

so

$m$