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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

(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°
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 start by noting that the given angles at point E must add up to 90 degrees since angle D E F measures 90 degrees.

The measures of the angles are given as follows:

• Angle D E G = (2x) degrees
• Angle G E F = (5x - 22) degrees

The sum of these two angles must equal the measure of the right angle (90 degrees):

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

Combining the terms gives us:

\[ 7x - 22 = 90 \]

To represent this as a simplified equation corresponding to the measures of the angles, we can rearrange it:

Thus, the correct response is:

\[ (7x - 22)° = 90° \]

So, the answer is (7x−22)°=90°. (Note: This particular option does not appear in your provided choices, suggesting a potential oversight in the problem setup or the options listed.)

If you meant to identify which of the provided equations could relate to the angles described, the corresponding angle equation of angles summing to a right angle from the choices would be:

(7x−22)°=90°. (if available in options)