Question 1

Question

A)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)°=180°
left parenthesis 1 x plus 1 right parenthesis degrees equals 180 degrees

(7x+1)°=90°
left parenthesis 7 x plus 1 right parenthesis degrees equals 90 degrees

(1x+1)°=90°
left parenthesis 1 x plus 1 right parenthesis degrees equals 90 degrees

(7x+1)°=180°
left parenthesis 7 x plus 1 right parenthesis degrees equals 180 degrees
Question 2
A)
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

(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°
left parenthesis 7 x minus 22 right parenthesis degrees equals 180 degrees

(3x−22)°=90°
left parenthesis 3 x minus 22 right parenthesis degrees equals 90 degrees
Question 3
A)
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

50
50

10
10

65
65

13
13
Question 4
A)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

30° and 60°
30 degrees and 60 degrees

19° and 71°
19 degrees and 71 degrees

33° and 57°
33 degrees and 57 degrees
Question 5
A)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

6
6

50
50

60
60

Answer 1

Here are the answers to the questions based on the information provided:

Question 1

A) 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?

Answer: (7x+1)°=90°
Explanation: Complementary angles sum to 90°. Therefore, the equation is:
\(3x + (4x + 1) = 90 \rightarrow 7x + 1 = 90\).

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Question 2

A) What is the simplified equation corresponding to the measures of the angles formed by rays D, G, and F?

Answer: (7x−22)°=90°
Explanation: The angles D E G and G E F add up to angle D E F, which measures 90°. Therefore:
\((2x) + (5x - 22) = 90 \rightarrow 7x - 22 = 90\).

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Question 3

A) Solve for the value of x given that one angle measures 25 degrees and the other measures 5x degrees.

Answer: 50
Explanation: Since the angles are complementary, we have:
\(25 + 5x = 90\),
Therefore, \(5x = 90 - 25 = 65\) then \(x = 65/5 = 13\).

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Question 4

A) What are the two angle measures of complementary angles expressed as 3x° and (2x−5)°?

Answer: 33° and 57°
Explanation: The angles must sum up to 90°:
\(3x + (2x - 5) = 90\) leads to \(5x - 5 = 90 \rightarrow 5x = 95 \rightarrow x = 19\).
Calculating the angles:
\(3(19) = 57°\) and \(2(19) - 5 = 33°\).

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Question 5

A) 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?

Answer: 6
Explanation: The angles are complementary, so:
\(40 + (8x + 2) = 90\) leads to \(8x + 42 = 90\) which gives \(8x = 48\), and thus \(x = 6\).

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