Question

In AEFG, ZE = (5x + 6)", mZF = (4x – 6)", and mZG = (5x – 2). Find
mZG.

Answer 1

`\boxed {\boxed {\sf m \angle G = 63}}`

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.

`(5x+6)+(4x-6)+(5x-2)= 180`

Combine like terms on the left side.

`(5x+4x+5x) + (6 + -6 -2) = 180`

`14x -2 = 180`

Solve for x. 2 is being subtracted from 14x. The inverse operation of subtraction is addition. Add 2 to both sides.

`14x-2+2=180+2 \\14x=182`

x is being multiplied by 14. The inverse operation of multiplication is division. Divide both sides by 14.

`\frac {14x}{14} = (182)/(14)`

`x= (182)/(14)`

`x=13`

Find the measure of angle G. Substitute x into the original expression.

`m \angle G =5x-2`

`m \angle G = 5 (13)-2\\m\angle G = 65-2 \\m\angle G = 63`

The measure of angle G is 63 degrees.