Answer:
[tex]\boxed {\boxed {\sf m \angle G = 63}}[/tex]
Step-by-step explanation:
The angles in a triangle add to 180 degrees.
We are given triangle EFG. There are 3 angles: m∡E = 5x+6, m∡F = 4x-6, and m∡G = 5x-2.
The sum of these three angles must equal 180. Set up an equation and solve for x.
[tex](5x+6)+(4x-6)+(5x-2)= 180[/tex]
Combine like terms on the left side.
[tex](5x+4x+5x) + (6 + -6 -2) = 180[/tex]
[tex]14x -2 = 180[/tex]
Solve for x. 2 is being subtracted from 14x. The inverse operation of subtraction is addition. Add 2 to both sides.
[tex]14x-2+2=180+2 \\14x=182[/tex]
x is being multiplied by 14. The inverse operation of multiplication is division. Divide both sides by 14.
[tex]\frac {14x}{14} = \frac{182}{14}[/tex]
[tex]x= \frac{182}{14}[/tex]
[tex]x=13[/tex]
Find the measure of angle G. Substitute x into the original expression.
[tex]m \angle G =5x-2[/tex]
[tex]m \angle G = 5 (13)-2\\m\angle G = 65-2 \\m\angle G = 63[/tex]
The measure of angle G is 63 degrees.
