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nataly862011 [7]
3 years ago
8

Given: measure of angle KJ = 124°, measure of IC =38° Find: m∠CQJ, m∠LIJ.

Mathematics
1 answer:
VLD [36.1K]3 years ago
3 0

Answer:

Part 1) m

Part 2) m

Step-by-step explanation:

Part 1) Find the measure of angle CQJ

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite.

m

arc\ IK+arc\ CJ=360\°-(arc\ IC+arc\ KJ)

substitute the values

arc\ IK+arc\ CJ=360\°-(38\°+124\°)=198\°

m

Part 2) Find the measure of angle LIJ

step 1

Find the measure of angle IJL

we know that

The inscribed angle is half that of the arc it comprises.

m

substitute the values

m

step 2

Find the measure of angle ILJ

we know that

The measurement of the external angle is the semi-difference of the arcs it encompasses.

m

substitute the values

m

step 3

Find the measure of angle LIJ

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

In the triangle LIJ

m

substitute the values

m

m

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