Two adjacent angles are on a straight line. One angle has a measure of (5x−28)° and the other angle has a measure of (8x)° . What is the measure of the second angle?(1 point)

Question

Responses

120°
120 degrees

52°
52 degrees

16°
16 degrees

128°

Answer 1

To solve the problem, you need to set up an equation. Since the two angles are adjacent and on a straight line, their measures must add up to 180 degrees (the sum of angles on a straight line is 180 degrees).

So, the equation is:

(5x - 28) + (8x) = 180

Combine like terms:

13x - 28 = 180

Add 28 to both sides:

13x = 208

Divide by 13:

x = 16

Now substitute the value of x back into the second angle's measure:

8x = 8(16) = 128

Therefore, the measure of the second angle is 128 degrees.

Answer 2

For two adjacent angles with measures x° and (x+30)° that make up a 90° angle, what is x ?(1 point)
Responses

60
60

15
15

30
30

20

Answer 3

To solve the problem, you need to set up an equation. Since the two angles are adjacent and make up a 90 degree angle, their measures must add up to 90 degrees.

So, the equation is:

x + (x + 30) = 90

Combine like terms:

2x + 30 = 90

Subtract 30 from both sides:

2x = 60

Divide by 2:

x = 30

Therefore, x is equal to 30.

Answer 4

Question
A right angle is formed by two adjacent angles with measures of (x)° and (x+30)° . What are the two angle measures?(1 point)
Responses

75° and 105°
75 degrees and 105 degrees

70° and 25°
70 degrees and 25 degrees

30° and 60°
30 degrees and 60 degrees

60° and 90°

Answer 5

To solve the problem, we know that the two angles must add up to 90 degrees since they form a right angle.

So, the equation is:

x + (x + 30) = 90

Combine like terms:

2x + 30 = 90

Subtract 30 from both sides:

2x = 60

Divide by 2:

x = 30

So, the measure of the first angle is x° = 30°.

To find the measure of the second angle (x + 30)°, we can substitute the value of x back into the equation:

30 + 30 = 60

So, the measure of the second angle is (x + 30)° = 60°.

Therefore, the two angle measures are 30° and 60°.

Answer 6

A 180° angle (straight line) is formed by two adjacent angles. One angle has a measure of (2x+3)° and the other has a measure of (x−6)°. What are the measures of the two angles that make up the straight line?(1 point)
Responses

125° and 55°
125 degrees and 55 degrees

186° and 88°
186 degrees and 88 degrees

121° and 59°
121 degrees and 59 degrees

129° and 51°

Answer 7

To solve the problem, we know that the sum of the measures of the two adjacent angles forming a straight line is 180 degrees.

So, the equation is:

(2x + 3) + (x - 6) = 180

Combine like terms:

3x - 3 = 180

Add 3 to both sides:

3x = 183

Divide by 3:

x = 61

Now, substitute the value of x back into the expressions for the angles:

Angle 1 = (2x + 3)° = (2*61 + 3)° = 125°

Angle 2 = (x - 6)° = (61 - 6)° = 55°

Therefore, the measures of the two angles that make up the straight line are 125° and 55°.

Answer 8

An obtuse angle is formed by two adjacent angles with measures (x−5)° and (3x)°. If the resulting angle measure is 107°, what is the angle measure of each of the two unknown angles? Round to the nearest whole number.(1 point)
Responses

28° and 79°
28 degrees and 79 degrees

20° and 87°
20 degrees and 87 degrees

23° and 84°
23 degrees and 84 degrees

32° and 75°
32 degrees and 75 degrees

Answer 9

To solve the problem, we need to set up an equation. Since the obtuse angle formed by the two adjacent angles is given as 107 degrees, we have:

(x - 5) + (3x) = 107

Combine like terms:

4x - 5 = 107

Add 5 to both sides:

4x = 112

Divide by 4:

x = 28

Now, substitute the value of x back into the expressions for the angles:

Angle 1 = (x - 5)° = (28 - 5)° = 23°

Angle 2 = (3x)° = (3 * 28)° = 84°

Therefore, the angle measures of the two unknown angles are 23° and 84°.