Question

Question

Use the image to answer the 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)°=90°
left parenthesis 7 x minus 22 right parenthesis degrees equals 90 degrees

(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

(3x−22)°=90°

Answer 1

To find the correct equation corresponding to the measures of the angles, we start by noting the relationships between the angles at point E.

1. We know that angle D E F measures 90 degrees.
2. The angles D E G and G E F can be expressed in terms of \(x\):
   • Angle D E G measures \(2x\) degrees.
   • Angle G E F measures \(5x - 22\) degrees.

Since the angles D E G and G E F together sum up to 90 degrees (since they make up the right angle D E F), we can set up the equation as follows:

\[ D E G + G E F = 90° \]

Substituting the expressions for the angles:

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

Combining these terms:

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

This simplifies to:

\[ 7x - 22 = 90 \]

So the corresponding equation is:

\[ (7x - 22)° = 90° \]

The correct response is:

(7x−22)°=90°