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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

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

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

(3x−22)°=90°
left parenthesis 3 x minus 22 right parenthesis degrees equals 90 degrees

(7x−22)°=90°

Answer 1

To find the simplified equation corresponding to the measures of the angles, we know the following:

• Angle D E F is a right angle, so it measures 90 degrees.
• The angles D E G and G E F can be expressed in terms of \( x \):
  • Angle D E G = \( 2x \) degrees
  • Angle G E F = \( 5x - 22 \) degrees

Since angle D E F is composed of angles D E G and G E F, we can set up the equation:

\[ \text{Angle D E G} + \text{Angle G E F} = \text{Angle D E F} \]

Substituting the values we have:

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

This simplifies to:

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

Combining like terms gives:

\[ 7x - 22 = 90 \]

Now we rearrange it to match one of the given responses.

Thus, the correct equation based on our simplifications is:

(7x−22)°=90°.

So the answer is:

(7x−22)°=90°.