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

The measure of angle G is
`53\°`

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\°`