In triangle FGH, if the measure of angle G is five less than twice the measure of angle F and the measure of angle H is eighteen less than four times the measure of angle F, find the measure of angle G.

Accepted Solution

Answer:The measure of angle G is [tex]53\°[/tex]Step-by-step explanation:LetF ----> the measure of interior angle F of the triangle FGHG ---> the measure of interior angle G of the triangle FGHH ---> the measure of interior angle H of the triangle FGHwe know thatThe sum of the interior angles in a triangle must be equal to 180 degreesso[tex]F+G+H=180\°[/tex] ----> equation A[tex]G=2F-5[/tex] ----> equation B[tex]H=4F-18[/tex] ----> equation CSolve the system of equations by substitutionsubstitute equation B and equation C in equation A[tex]F\°+(2F-5)\°+(4F-18)\°=180\°[/tex]Solve for F[tex]7F-23=180[/tex][tex]7F=180+23[/tex][tex]F=29\°[/tex]Find the measure of angle G[tex]G=2F-5[/tex]substitute the value of F[tex]G=2(29)-5=53\°[/tex]