Solve Equations with Complementary Angles Quick Check

Question

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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?

Answer 1

Given the information in the question, we can write the equation for the measures of the angles as follows:

Angle DEF + Angle DEG + Angle GEF = 90 degrees

Substituting the given angle measures, we have:

90 + 2x + (5x - 22) = 90

Simplifying the equation gives:

2x + 5x - 22 = 0

Combining like terms:

7x - 22 = 0

Adding 22 to both sides:

7x = 22

Finally, dividing both sides by 7 gives the simplified equation:

x = 22/7