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?
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