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

(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

(7x−22)°=90°

Answer 1

To find the simplified equation that corresponds to the measures of the angles, we need to analyze the angles at point E.

Given:

• Angle D E F measures 90 degrees.
• Angle D E G measures (2x) degrees.
• Angle G E F measures (5x - 22) degrees.

Since Angle D E F is the right angle formed by the rays, the sum of Angle D E G and Angle G E F must also equal 90 degrees:

\[ \text{Angle D E G} + \text{Angle G E F} = 90° \] \[ (2x) + (5x - 22) = 90 \]

Now we can simplify this equation:

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

To form a simplified equation corresponding to the angles, we can set this equal to 90 degrees:

So, the correct equation is: \[ (7x - 22)° = 90° \]

Thus, the answer is:

(7x−22)°=90° (7x−22 degrees equals 90 degrees)