1) Given: mLHE=84°Find: m∠EYL. 2)Given: m∠EYL=72°Find: m arc EHL, m arc LVE
Accepted Solution
A:
Answer:Part 1) The measure of angle EYL is [tex]96\°[/tex]Part 2) The measure of arc EHL is [tex]108\°[/tex] and the measure of arc LVE is [tex]252\°[/tex]Step-by-step explanation:we know thatThe measurement of the outer angle is the semi-difference of the arcs which comprisesPart 1) Letx------> the measure of arc LHEy----> the measure of arc LVEwe know that[tex]x+y=360\°[/tex][tex]x=84\°[/tex]Find the value of y[tex]y=360\°-84\°=276\°[/tex]Find the measure of angle EYL[tex]m<EYL=\frac{1}{2} (y-x)[/tex]substitute the values[tex]m<EYL=\frac{1}{2}(276\°-84\°)=96\°[/tex]Part 2)Letx------> the measure of arc EHLy----> the measure of arc LVEwe know that[tex]x+y=360\°[/tex] [tex]x=360\°-y[/tex] -----> equation A[tex]m<EYL=72\°[/tex][tex]m<EYL=\frac{1}{2} (y-x)[/tex]substitute[tex]72\°=\frac{1}{2} (y-x)[/tex][tex]144\°=(y-x)[/tex][tex]x=y-144\°[/tex] --------> equation Bequate equation A and equation B and solve for y[tex]360\°-y=y-144\°[/tex][tex]2y=360\°+144\°[/tex][tex]2y=504\°[/tex][tex]y=252\°[/tex]Find the value of x[tex]x=252\°-144\°=108\°[/tex]thereforeThe measure of arc EHL is [tex]108\°[/tex]The measure of arc LVE is [tex]252\°[/tex]