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

(3x−22)°=90°
left parenthesis 3 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
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Answer 1

To find the simplified equation corresponding to the measures of the angles, we start with the given information:

• Angle \( D E F = 90^\circ \)
• Angle \( D E G = (2x)^\circ \)
• Angle \( G E F = (5x - 22)^\circ \)

Since the angles D E G and G E F together must equal the right angle at E (which is also 90 degrees since \( D E F \) measures 90 degrees), we can set up the equation:

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

Combining like terms gives:

\[ 7x - 22 = 90 \]

This simplifies to:

\[ (7x - 22)° = 90° \]

Thus, the correct response is:

(7x−22)°=90°