two adjacent angles are on a straight line. one angle has a measure of (5x - 28) and the other angle has ameasure of (8x) what is the measure of the second angle
Since the two angles are adjacent and lie on a straight line, their sum must be 180 degrees. Therefore, we can set up the equation:
(5x - 28) + (8x) = 180
Combining like terms:
13x - 28 = 180
Add 28 to both sides:
13x = 208
Divide both sides by 13:
x = 16
Now we can find the measure of the second angle:
Second angle = 8x = 8(16) = 128
Therefore, the measure of the second angle is 128 degrees.
for two adjacent angles with measurs x and (x+30) that make up a 90 angle what is x?
Since the two adjacent angles make up a 90-degree angle, their sum must be 90 degrees. Therefore, we can set up the equation:
x + (x + 30) = 90
Combine like terms:
2x + 30 = 90
Subtract 30 from both sides:
2x = 60
Divide both sides by 2:
x = 30
Therefore, x is equal to 30.
a right angle is formed by two adjacent angles with measures of (x) and (x+30) what are the two angle measurments
Since a right angle measures 90 degrees, we can set up the equation:
x + (x + 30) = 90
Combining like terms:
2x + 30 = 90
Subtract 30 from both sides:
2x = 60
Divide both sides by 2:
x = 30
So, one angle measures x = 30 degrees.
The other angle measures (x + 30) = (30 + 30) = 60 degrees.
Therefore, the two angle measurements are 30 degrees and 60 degrees.
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?
Since the two adjacent angles make up a straight line (180 degrees), their sum must be 180 degrees. Therefore, we can set up the equation:
(2x + 3) + (x - 6) = 180
Combining like terms:
3x - 3 = 180
Add 3 to both sides:
3x = 183
Divide both sides by 3:
x = 61
Now we can find the measures of the two angles:
First angle: (2x + 3) = (2 * 61 + 3) = 125 degrees
Second angle: (x - 6) = (61 - 6) = 55 degrees
Therefore, the measures of the two angles that make up the straight line are 125 degrees and 55 degrees.
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.
Since an obtuse angle measures between 90 and 180 degrees, we can set up the equation:
(x-5) + (3x) = 107
Combine like terms:
4x - 5 = 107
Add 5 to both sides:
4x = 112
Divide both sides by 4:
x = 28
Now we can find the measures of the two angles:
First angle: (x-5) = (28 - 5) = 23 degrees
Second angle: (3x) = (3 * 28) = 84 degrees
Therefore, the angle measures of the two unknown angles are 23 degrees and 84 degrees.