Question

Solve Equations with Complementary Angles Quick Check
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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

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

(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
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Answer 1

To find the simplified equation corresponding to the measures of the angles formed by rays D, G, and F at point E, we need to work with the information given:

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

Since angles D E G and G E F together make up the right angle D E F, we can set up the equation:

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

Now, combining like terms:

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

This simplifies to:

\[
7x - 22 = 90
\]

So the corresponding equation is:

\[
(7x - 22)^\circ = 90^\circ
\]

Therefore, the correct response is:

**(7x−22)°=90°**