The sum of two adjacent angles on a straight line is equal to 180 degrees.
So, we have the equation:
(5x - 28) + (8x) = 180
Combining like terms:
13x - 28 = 180
Adding 28 to both sides:
13x = 208
Dividing both sides by 13:
x = 16
Substituting x = 16 into the expression for the second angle:
8x = 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 128° 128 degrees 16°
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 30 30 15 15 60
For two adjacent angles that make up a 90° angle, their sum must equal 90°.
So, we have the equation:
x + (x + 30) = 90
Combining like terms:
2x + 30 = 90
Subtracting 30 from both sides:
2x = 60
Dividing both sides by 2:
x = 30
Therefore, x = 30.
So, we have the equation:
x + (x + 30) = 90
Combining like terms:
2x + 30 = 90
Subtracting 30 from both sides:
2x = 60
Dividing both sides by 2:
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 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°
A right angle measures 90°.
Therefore, we have the equation:
x + (x + 30) = 90
Combining like terms:
2x + 30 = 90
Subtracting 30 from both sides:
2x = 60
Dividing both sides by 2:
x = 30
So, one angle measures 30° and the other angle measures (30 + 30) = 60°.
Therefore, the two angle measures are 30° and 60°.
Therefore, we have the equation:
x + (x + 30) = 90
Combining like terms:
2x + 30 = 90
Subtracting 30 from both sides:
2x = 60
Dividing both sides by 2:
x = 30
So, one angle measures 30° and the other angle measures (30 + 30) = 60°.
Therefore, 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 125° and 55° 125 degrees and 55 degrees 121° and 59° 121 degrees and 59 degrees 186° and 88° 186 degrees and 88 degrees 129° and 51° 129 degrees and 51 degrees
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
Combining like terms:
3x - 3 = 180
Adding 3 to both sides:
3x = 183
Dividing both sides by 3:
x = 61
Substituting x = 61 into the expressions for the angles:
1st angle = 2x + 3 = 2(61) + 3 = 123 + 3 = 126°
2nd angle = x - 6 = 61 - 6 = 55°
Therefore, the measures of the two angles that make up the straight line are 126° and 55°.
(2x + 3) + (x - 6) = 180
Combining like terms:
3x - 3 = 180
Adding 3 to both sides:
3x = 183
Dividing both sides by 3:
x = 61
Substituting x = 61 into the expressions for the angles:
1st angle = 2x + 3 = 2(61) + 3 = 123 + 3 = 126°
2nd angle = x - 6 = 61 - 6 = 55°
Therefore, the measures of the two angles that make up the straight line are 126° 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 23° and 84° 23 degrees and 84 degrees 28° and 79° 28 degrees and 79 degrees 32° and 75° 32 degrees and 75 degrees 20° and 87°
To find the angle measures of each of the two unknown angles, we need to set up the equation:
(x - 5) + (3x) = 107
Combining like terms:
4x - 5 = 107
Adding 5 to both sides:
4x = 112
Dividing both sides by 4:
x = 28
Substituting x = 28 into the expressions for the angles:
1st angle = x - 5 = 28 - 5 = 23°
2nd angle = 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
Substituting x = 28 into the expressions for the angles:
1st angle = x - 5 = 28 - 5 = 23°
2nd angle = 3x = 3(28) = 84°
Therefore, the angle measures of the two unknown angles are 23° and 84°.
9 answers