To find the measure of the second angle, we can set up the equation 5x - 28 + 8x = 180, since the sum of the two adjacent angles on a straight line is 180 degrees.
Combining like terms, we have 13x - 28 = 180.
Adding 28 to both sides, we get 13x = 208.
Dividing both sides by 13, we find x = 16.
Substituting x = 16 into 8x, we get 8(16) = 128.
Therefore, the measure of the second angle is 128 degrees.
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
120°
120 degrees
16°
16 degrees
128°
9 answers
For two adjacent angles with measures x° and (x+30)° that make up a 90° angle, what is x ?(1 point)
Responses
20
20
60
60
15
15
30
Responses
20
20
60
60
15
15
30
To find the measure of x, we need to set up the equation x + (x+30) = 90, since the two adjacent angles make up a 90° angle.
Combining like terms, we have 2x + 30 = 90.
Subtracting 30 from both sides, we get 2x = 60.
Dividing both sides by 2, we find x = 30.
Therefore, x = 30.
Combining like terms, we have 2x + 30 = 90.
Subtracting 30 from both sides, we get 2x = 60.
Dividing both sides by 2, we find x = 30.
Therefore, x = 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
70° and 25°
70 degrees and 25 degrees
60° and 90°
60 degrees and 90 degrees
75° and 105°
75 degrees and 105 degrees
30° and 60°
Responses
70° and 25°
70 degrees and 25 degrees
60° and 90°
60 degrees and 90 degrees
75° and 105°
75 degrees and 105 degrees
30° and 60°
To form a right angle, the sum of the measures of the two adjacent angles should be 90°.
Setting up the equation x + (x+30) = 90, we can solve for x.
Combining like terms, we have 2x + 30 = 90.
Subtracting 30 from both sides, we get 2x = 60.
Dividing both sides by 2, we find x = 30.
Therefore, the two angle measures are x = 30° and (x+30) = 60°.
So, the two angle measures are 30° and 60°.
Setting up the equation x + (x+30) = 90, we can solve for x.
Combining like terms, we have 2x + 30 = 90.
Subtracting 30 from both sides, we get 2x = 60.
Dividing both sides by 2, we find x = 30.
Therefore, the two angle measures are x = 30° and (x+30) = 60°.
So, the two angle measures are 30° and 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
121° and 59°
121 degrees and 59 degrees
186° and 88°
186 degrees and 88 degrees
125° and 55°
125 degrees and 55 degrees
129° and 51°
Responses
121° and 59°
121 degrees and 59 degrees
186° and 88°
186 degrees and 88 degrees
125° and 55°
125 degrees and 55 degrees
129° and 51°
To find the measures of the two angles that make up the straight line, we need to set up the equation (2x+3) + (x-6) = 180, since the sum of the two adjacent angles on a straight line is 180°.
Combining like terms, we have 3x - 3 = 180.
Adding 3 to both sides, we get 3x = 183.
Dividing both sides by 3, we find x = 61.
Substituting x = 61 into (2x+3), we get 2(61) + 3 = 122 + 3 = 125.
Substituting x = 61 into (x-6), we get 61 - 6 = 55.
Therefore, the measures of the two angles that make up the straight line are 125° and 55°.
Combining like terms, we have 3x - 3 = 180.
Adding 3 to both sides, we get 3x = 183.
Dividing both sides by 3, we find x = 61.
Substituting x = 61 into (2x+3), we get 2(61) + 3 = 122 + 3 = 125.
Substituting x = 61 into (x-6), we get 61 - 6 = 55.
Therefore, the measures of 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
28° and 79°
28 degrees and 79 degrees
32° and 75°
32 degrees and 75 degrees
23° and 84°
23 degrees and 84 degrees
20° and 87°
Responses
28° and 79°
28 degrees and 79 degrees
32° and 75°
32 degrees and 75 degrees
23° and 84°
23 degrees and 84 degrees
20° and 87°
To find the angle measures, we need to set up the equation (x-5) + (3x) = 107, since the sum of the two adjacent angles forms the obtuse angle of 107°.
Combining like terms, we have 4x - 5 = 107.
Adding 5 to both sides, we get 4x = 112.
Dividing both sides by 4, we find x = 28.
Substituting x = 28 into (x-5), we get 28 - 5 = 23.
Substituting x = 28 into (3x), we get 3(28) = 84.
Therefore, the angle measures are 23° and 84°.
Combining like terms, we have 4x - 5 = 107.
Adding 5 to both sides, we get 4x = 112.
Dividing both sides by 4, we find x = 28.
Substituting x = 28 into (x-5), we get 28 - 5 = 23.
Substituting x = 28 into (3x), we get 3(28) = 84.
Therefore, the angle measures are 23° and 84°.
9 answers