Question

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

Answer 1

Answer:

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

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.

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

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.

$\frac {14x}{14} = \frac{182}{14}$

$x= \frac{182}{14}$

$x=13$

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.