Question

Question 1
A)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)
Responses

52°
52 degrees

128°
128 degrees

120°
120 degrees

16°
16 degrees
Question 2
A)For two adjacent angles with measures x°
and (x+30)°
that make up a 90°
angle, what is x
?(1 point)
Responses

30
30

60
60

20
20

15
15
Question 3
A)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

30°
and 60°
30 degrees and 60 degrees

60°
and 90°
60 degrees and 90 degrees

75°
and 105°
75 degrees and 105 degrees

70°
and 25°
70 degrees and 25 degrees
Question 4
A)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

186°
and 88°
186 degrees and 88 degrees

129°
and 51°
129 degrees and 51 degrees

125°
and 55°
125 degrees and 55 degrees

121°
and 59°
121 degrees and 59 degrees
Question 5
A)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

32°
and 75°
32 degrees and 75 degrees

28°
and 79°
28 degrees and 79 degrees

23°
and 84°
23 degrees and 84 degrees

20°
and 87°
20 degrees and 87 degrees

Answer 1

Let's solve each question step by step.

### Question 1
Two adjacent angles are on a straight line. One angle is \((5x−28)°\) and the other is \((8x)°\).

The sum of angles on a straight line is \(180°\):
\[
(5x - 28) + (8x) = 180
\]
\[
13x - 28 = 180
\]
\[
13x = 208
\]
\[
x = \frac{208}{13} = 16
\]

Now, substitute \(x\) back into the second angle:
\[
8x = 8(16) = 128°
\]

**Response:** 128°

### Question 2
For two adjacent angles with measures \(x°\) and \((x + 30)°\) that make up a \(90°\) angle, we have:
\[
x + (x + 30) = 90
\]
\[
2x + 30 = 90
\]
\[
2x = 60
\]
\[
x = 30
\]

**Response:** 30

### Question 3
A right angle is formed by two adjacent angles with measures of \(x°\) and \((x + 30)°\).

Since the sum is \(90°\):
\[
x + (x + 30) = 90
\]
\[
2x + 30 = 90
\]
\[
2x = 60
\]
\[
x = 30
\]

Thus, the two angle measures are:
\[
30° \text{ and } 60°
\]

**Response:** 30° and 60°

### Question 4
A \(180°\) angle (straight line) is formed by two adjacent angles. One angle is \((2x + 3)°\) and the other is \((x - 6)°\).

Setting up the equation:
\[
(2x + 3) + (x - 6) = 180
\]
\[
3x - 3 = 180
\]
\[
3x = 183
\]
\[
x = 61
\]

Now substitute \(x\) back into the angle measures:
First angle:
\[
2x + 3 = 2(61) + 3 = 125°
\]
Second angle:
\[
x - 6 = 61 - 6 = 55°
\]

**Response:** 125° and 55°

### Question 5
An obtuse angle is formed by two adjacent angles with measures \((x - 5)°\) and \((3x)°\). If the resulting angle measure is \(107°\):
\[
(x - 5) + (3x) = 107
\]
\[
4x - 5 = 107
\]
\[
4x = 112
\]
\[
x = 28
\]

Now substitute \(x\) back into the angle measures:
First angle:
\[
x - 5 = 28 - 5 = 23°
\]
Second angle:
\[
3x = 3(28) = 84°
\]

**Response:** 23° and 84°

Here are all the responses:
1. 128°
2. 30
3. 30° and 60°
4. 125° and 55°
5. 23° and 84°