in the circle below, f is the center, gi is the diameter and m

Accepted Solution

Answer:Part a) [tex]m<HIG=40\°[/tex]Part b) IHG is a semicircle and GJI is a semicirclePart c) HIJ is a major arc and HIJG is a major arcPart d) [tex]arc\ GH=80\°[/tex] Part e) [tex]arc\ GJI=180\°[/tex] Step-by-step explanation:Part a) Give an inscribed anglewe know thatThe inscribed angle measures half that of the arc comprisingso in this problem m<HIG is an inscribed angle[tex]m<HIG=\frac{1}{2}(arc\ HG)[/tex][tex]arc\ HG=80\°[/tex] ----> by central anglesubstitute[tex]m<HIG=\frac{1}{2}(80\°)=40\°[/tex]Part b) Give a semicirclewe know thatThe diameter divide the circle into two semicirclessoGI is a diameterthereforeIHG is a semicircleGJI is a semicirclePart c) Give a major arcwe know thatThe measure of a major arc is greater than 180 degreesthereforeHIJ is a major arcHIJG is a major arcPart d) Measure of arc GHwe know that[tex]arc\ GH=m<HFG[/tex] ----> by central angleso[tex]arc\ GH=80\°[/tex] Part e) Measure of arc GJIwe know that[tex]arc\ GJI=180\°[/tex] ----> the arc represent a semicircle