Solve Equations with Adjacent Angles Quick Check
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Question
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
To find the measure of the second angle, we can set up an equation.
Since the two angles are adjacent and on a straight line, they add up to 180 degrees.
So, we have:
(5x - 28) + (8x) = 180
Combining like terms, we get:
13x - 28 = 180
Adding 28 to both sides, we get:
13x = 208
Dividing both sides by 13, we get:
x = 16
Now we can substitute x back into the expression for the second angle, which is (8x):
Second angle = 8(16) = 128 degrees
Therefore, the measure of the second angle is 128 degrees.
The correct response is:
128°
128 degrees
Since the two adjacent angles make up a 90° angle, we can set up an equation:
x + (x + 30) = 90
Combining like terms, we get:
2x + 30 = 90
Subtracting 30 from both sides, we get:
2x = 60
Dividing both sides by 2, we get:
x = 30
So, x = 30.
The correct response is:
30
Since a right angle measures 90°, we can set up an equation:
x + (x + 30) = 90
Combining like terms, we get:
2x + 30 = 90
Subtracting 30 from both sides, we get:
2x = 60
Dividing both sides by 2, we get:
x = 30
So, the two angle measures are:
x = 30°
x + 30 = 30 + 30 = 60°
Therefore, the correct response is:
30° and 60°
30 degrees and 60 degrees
Since the two adjacent angles make up a 180° angle (straight line), we can set up an equation:
(2x + 3) + (x - 6) = 180
Combining like terms, we get:
3x - 3 = 180
Adding 3 to both sides, we get:
3x = 183
Dividing both sides by 3, we get:
x = 61
Now we can substitute x back into the expressions for the angle measures:
First angle = 2x + 3 = 2(61) + 3 = 122 + 3 = 125°
Second angle = x - 6 = 61 - 6 = 55°
Therefore, the measures of the two angles that make up the straight line are:
125° and 55°
The correct response is:
125° and 55°
125 degrees and 55 degrees
Since the two adjacent angles form an obtuse angle measuring 107°, we can set up an equation:
(x - 5) + (3x) = 107
Combining like terms, we get:
4x - 5 = 107
Adding 5 to both sides, we get:
4x = 112
Dividing both sides by 4, we get:
x = 28
Now we can substitute x back into the expressions for the angle measures:
First angle = x - 5 = 28 - 5 = 23°
Second angle = 3x = 3(28) = 84°
Therefore, the angle measures of the two unknown angles are:
23° and 84°
The correct response is:
23° and 84°
23 degrees and 84 degrees
Solve Equations with Adjacent Angles Quick Check
2 of 5 2 of 5 Items
Question
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
20
20
30
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
75° and 105°
75 degrees and 105 degrees
60° and 90°
60 degrees and 90 degrees
70° and 25°
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
121° and 59°
121 degrees and 59 degrees
125° and 55°
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
20° and 87°
20 degrees and 87 degrees
23° and 84°
23 degrees and 84 degrees
28° and 79°