MATH SOLVE

2 months ago

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

Accepted Solution

A:

Answer:Part 1) The measure of angle LIJ is [tex]m<LIJ=118\°[/tex]Part 2) The measure of angle CQJ is [tex]m<CQJ=99\°[/tex]Step-by-step explanation:step 1Find the measure of angle KIJwe know thatThe inscribed angle measures half that of the arc comprisingso[tex]m<KIJ=\frac{1}{2}(arc\ KJ)[/tex]substitute[tex]m<KIJ=\frac{1}{2}(124\°)=62\°[/tex]step 2Find the measure of angle LIJwe know that[tex]m<LIJ+m<KIJ=180\°[/tex] -----> by supplementary anglessubstitute[tex]m<LIJ+62\°=180\°[/tex][tex]m<LIJ=180\°-62\°=118\°[/tex]step 3 Find the measure of angle IKQwe know thatThe inscribed angle measures half that of the arc comprisingso[tex]m<IKQ=\frac{1}{2}(arc\ IC)[/tex][tex]m<IKQ=\frac{1}{2}(38\°)=19\°[/tex]step 4Find the measure of angle IQKRemember that the sum of the internal angles of a triangle must be equal to 180 degreesIn the triangle IQK[tex]m<IKQ+m<KIJ+m<IQK=180\°[/tex]substitute the values[tex]19\°+62\°+m<IQK=180\°[/tex][tex]m<IQK=180\°-(19\°+62\°)=99\°[/tex]step 5Find the measure of angle CQJwe know thatm<CQJ=m<IQK -----> by vertical anglesso[tex]m<CQJ=99\°[/tex]