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
(7x+1)°=180°
left parenthesis 7 x plus 1 right parenthesis degrees equals 180 degrees
(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
(1x+1)°=180°
(1x+1)°=180°
Solve Equations with Complementary Angles Quick Check
2 of 5 2 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)°=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)°=180°
left parenthesis 7 x minus 22 right parenthesis degrees equals 180 degrees
(7x−22)°=90°
left parenthesis 7 x minus 22 right parenthesis degrees equals 90 degrees
(7x−22)°=90°
Solve Equations with Complementary Angles Quick Check
3 of 5 3 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
65
65
50
50
10
10
13
13
To find the value of x, we can set up the equation:
25 + 5x = 90
Now we can solve for x by subtracting 25 from both sides:
5x = 65
Dividing both sides by 5:
x = 13
Therefore, the value of x is 13.
What are the two angle measures of complementary angles expressed as 3x° and (2x−5)° ?(1 point)
Responses
21° and 69°
21 degrees and 69 degrees
19° and 71°
19 degrees and 71 degrees
30° and 60°
30 degrees and 60 degrees
33° and 57
To find the two angle measures of complementary angles expressed as 3x° and (2x−5)°, we can set up the equation:
3x + (2x-5) = 90
Now we can solve for x:
5x - 5 = 90
5x = 95
x = 19
Substituting the value of x back into the expressions for the angle measures:
3(19) = 57°
2(19) - 5 = 33°
Therefore, the two angle measures are 57° and 33°.
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
11
11
50
50
6
6
60
To find the value of x, we can set up the equation:
40 + (8x + 2) = 90
Now we can solve for x by subtracting 40 from both sides:
8x + 2 = 50
Subtracting 2 from both sides:
8x = 48
Dividing both sides by 8:
x = 6
Therefore, the value of x is 6.