Use the image to answer the question.

Question

An illustration shows three rays D, G, and F emerging from a point labeled E, forming a right angle at E. The right angle is divided into two parts by ray E G. The angles face leftward. Angle D E F measures 90 degree, angle D E G measures left parenthesis 2 x right parenthesis degrees, and angle G E F measures left parenthesis 5 x minus 22 right parenthesis degrees.

What is the simplified equation corresponding to the measures of the angles?

(1 point)
Responses

(7x−22)°=180°
left parenthesis 7 x minus 22 right parenthesis degrees equals 180 degrees

(3x−22)°=180°
left parenthesis 3 x minus 22 right parenthesis degrees equals 180 degrees

(7x−22)°=90°
left parenthesis 7 x minus 22 right parenthesis degrees equals 90 degrees

(3x−22)°=90°

Answer 1

To find the equation that corresponds to the measures of the angles, we start with the information given in the illustration:

1. We know that angle D E F measures 90 degrees.
2. We have angle D E G measuring \(2x\) degrees.
3. And angle G E F measuring \(5x - 22\) degrees.

Since angles D E G and G E F together sum to angle D E F (which is 90 degrees), we can set up the equation:

\[ 2x + (5x - 22) = 90 \]

Simplifying the left side, we combine the terms:

\[ 2x + 5x - 22 = 90 \] \[ 7x - 22 = 90 \]

Thus, the simplified equation is:

\[ (7x - 22)° = 90° \]

So the correct response is: (7x−22)°=90°