Question

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.

Answer 1

Answer:

The measure of angle G is $53\°$

Step-by-step explanation:

Let

F ----> the measure of interior angle F of the triangle FGH

G ---> the measure of interior angle G of the triangle FGH

H ---> the measure of interior angle H of the triangle FGH

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

$F+G+H=180\°$ ----> equation A

$G=2F-5$ ----> equation B

$H=4F-18$ ----> equation C

Solve the system of equations by substitution

substitute equation B and equation C in equation A

$F\°+(2F-5)\°+(4F-18)\°=180\°$

Solve for F

$7F-23=180$

$7F=180+23$

$F=29\°$

Find the measure of angle G

$G=2F-5$

substitute the value of F

$G=2(29)-5=53\°$