Solve Equations with Complementary Angles Quick Check
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Question
Two angles are complementary. One angle has a measure of 40° and the other has a measure of (8x+2)°. What is the value of x?(1 point)
Responses
6
6
50
50
60
60
11
To find the value of x, we can set up an equation using the definition of complementary angles.
Two angles are complementary if their measures add up to 90 degrees.
So, we have the equation:
40 + (8x + 2) = 90
To solve for x, we can simplify the equation:
8x + 42 = 90
Subtract 42 from both sides of the equation:
8x = 48
Divide both sides by 8:
x = 6
Therefore, the value of x is 6.
Solve Equations with Complementary Angles Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
An illustration shows a right angle. A ray extends from the right angle to create complementary angles. One angle measures 25 degrees. The other angle measures 5 x degrees. The angles are not labeled.
Solve for the value of x .
(1 point)
Responses
13
13
10
10
65
65
50
50
Since we know that the two angles are complementary, their measures add up to 90 degrees.
We have the equation:
25 + 5x = 90
Subtract 25 from both sides:
5x = 65
Divide both sides by 5:
x = 13
Therefore, the value of x is 13.
Solve Equations with Complementary Angles Quick Check
2 of 52 of 5 Items
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
(3x−22)°=180°
left parenthesis 3 x minus 22 right parenthesis degrees equals 180 degrees
(7x−22)°=180°
To find the simplified equation corresponding to the measures of the angles, we can use the fact that a right angle measures 90 degrees.
The given information tells us that angle DEF measures 90 degrees, angle DEG measures 2x degrees, and angle GEF measures 5x-22 degrees.
Since the sum of the measures of the three angles in a right triangle is 90 degrees, we can write the equation:
90 = (2x) + (5x-22)
Simplifying the equation:
90 = 7x - 22
Add 22 to both sides:
112 = 7x
Divide both sides by 7:
16 = x
Therefore, the simplified equation corresponding to the measures of the angles is (7x-22)° = 90°.
Solve Equations with Complementary Angles Quick Check
1 of 51 of 5 Items
Question
A figure displays two nonadjacent angles with measures 3x° and (4x+1)°. If the angles are complementary, what is the simplified equation corresponding to the measures of the angles?(1 point)
Responses
(1x+1)°=90°
left parenthesis 1 x plus 1 right parenthesis degrees equals 90 degrees
(7x+1)°=90°
left parenthesis 7 x plus 1 right parenthesis degrees equals 90 degrees
(7x+1)°=180°
left parenthesis 7 x plus 1 right parenthesis degrees equals 180 degrees
(1x+1)°=180°
To find the simplified equation corresponding to the measures of the angles, we can use the fact that complementary angles add up to 90 degrees.
Given that the two nonadjacent angles measure 3x° and (4x+1)°, we can set up the equation:
3x + (4x+1) = 90
Simplifying the equation:
7x + 1 = 90
Subtracting 1 from both sides:
7x = 89
Dividing both sides by 7:
x = 89/7
Therefore, the simplified equation corresponding to the measures of the angles is (7x+1)°=90°.