Question

In the given figure, mHJ = 106° and F H G Figure not drawn to scale FH ~JH. Which statement is true? K 106° J OA. The measure of ZG is 21°, and triangle FGH is isosceles. OB. The measure of ZG is 56°, and triangle FGH is isosceles. OC. The measure of ZG is 21°, and triangle FGH is not isosceles The measure of ZG is 56°, and triangle FGH is not isoscelesd D.​

Answer 1

Check the picture below.

`\measuredangle G=\cfrac{\stackrel{far~arc}{148}-\stackrel{near~arc}{106}}{2}\implies \measuredangle G=21^o \\\\\\ \hspace{6em}\measuredangle F=\cfrac{106}{2}\implies \measuredangle F=53^o\hspace{8em}\measuredangle G=106^o \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle FGH\textit{ is not an isosceles}~\hfill`