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
60° and 90°
60 degrees and 90 degrees
70° and 25°
70 degrees and 25 degrees
30° and 60°
30 degrees and 60 degrees
75° and 105°
9 answers
The correct answer is 60° and 90°.
For two adjacent angles with measures x° and (x+30)° that make up a 90° angle, what is x ?(1 point)
Responses
20
20
30
30
60
60
15
Responses
20
20
30
30
60
60
15
The correct answer is 60.
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°
Responses
186° and 88°
186 degrees and 88 degrees
129° and 51°
129 degrees and 51 degrees
125° and 55°
To find the measures of the two angles that make up a straight line of 180°, we can set up an equation:
(2x + 3) + (x - 6) = 180
Simplifying the equation:
3x - 3 = 180
Adding 3 to both sides:
3x = 183
Dividing both sides by 3:
x = 61
Now, we can substitute the value of x back into the equations to find the measures of the angles:
(2x + 3) = (2(61) + 3) = 125°
(x - 6) = (61 - 6) = 55°
The two angles that make up the straight line are 125° and 55°.
(2x + 3) + (x - 6) = 180
Simplifying the equation:
3x - 3 = 180
Adding 3 to both sides:
3x = 183
Dividing both sides by 3:
x = 61
Now, we can substitute the value of x back into the equations to find the measures of the angles:
(2x + 3) = (2(61) + 3) = 125°
(x - 6) = (61 - 6) = 55°
The two angles that make up the straight line are 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
20° and 87°
20 degrees and 87 degrees
32° and 75°
32 degrees and 75 degrees
28° and 79°
28 degrees and 79 degrees
23° and 84°
Responses
20° and 87°
20 degrees and 87 degrees
32° and 75°
32 degrees and 75 degrees
28° and 79°
28 degrees and 79 degrees
23° and 84°
To find the angle measures, we can set up an equation based on the given information:
(x - 5)° + (3x)° = 107°
Combining like terms:
4x - 5 = 107
Adding 5 to both sides:
4x = 112
Dividing both sides by 4:
x = 28
Now, we can substitute the value of x back into the equations to find the measures of the angles:
(x - 5)° = (28 - 5)° = 23°
(3x)° = (3(28))° = 84°
Therefore, the angle measures of the two unknown angles are 23° and 84°.
(x - 5)° + (3x)° = 107°
Combining like terms:
4x - 5 = 107
Adding 5 to both sides:
4x = 112
Dividing both sides by 4:
x = 28
Now, we can substitute the value of x back into the equations to find the measures of the angles:
(x - 5)° = (28 - 5)° = 23°
(3x)° = (3(28))° = 84°
Therefore, the angle measures of the two unknown angles are 23° and 84°.
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°
Responses
52°
52 degrees
128°
128 degrees
120°
120 degrees
16°
To find the measure of the second angle, we can set up an equation based on the given information:
(5x - 28)° + (8x)° = 180°
Combining like terms:
13x - 28 = 180
Adding 28 to both sides:
13x = 208
Dividing both sides by 13:
x = 16
Now, we can substitute the value of x back into the equation to find the measure of the second angle:
(8x)° = (8 * 16)° = 128°
Therefore, the measure of the second angle is 128°.
(5x - 28)° + (8x)° = 180°
Combining like terms:
13x - 28 = 180
Adding 28 to both sides:
13x = 208
Dividing both sides by 13:
x = 16
Now, we can substitute the value of x back into the equation to find the measure of the second angle:
(8x)° = (8 * 16)° = 128°
Therefore, the measure of the second angle is 128°.
1 answer