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

Answer 1

Given that rays D, G, and F form a right angle at point E, we know that the sum of the angles D E G and G E F must equal 90 degrees because they together form the right angle D E F. We are given:

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

The equation to represent the relationship between these angles is:

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

Now, let's simplify this equation:

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

So the equation corresponding to the measures of the angles, simplified, is:

\[
(7x - 22)° = 90°
\]

Thus, the correct response is:

\((7x - 22)° = 90°\)