For two adjacent angles with measures x° and (x+30)° that make up a 90° angle, what is x ?
To find the value of x, we need to use the fact that the sum of the measures of the two adjacent angles that make up a 90° angle is 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°.
A right angle is formed by two adjacent angles with measures of (x)° and (x+30)° . What are the two angle measures?
If a right angle is formed by two adjacent angles, it means that the sum of their measures is 90 degrees.
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, one angle measure is 30 degrees.
To find the other angle measure, we substitute x with its value:
(x + 30) = (30 + 30) = 60
Therefore, the two angle measures 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?
If a straight line angle is formed by two adjacent angles, it means that the sum of their measures is 180 degrees.
So, we have 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
Now, we can substitute the value of x back into the expressions for the angle measures:
2x + 3 = 2(61) + 3 = 122 + 3 = 125 degrees
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 we are given that the resulting angle measure is 107°, we can 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
Now, we can substitute the value of x back into the expressions for the angle measures:
(x - 5) = 28 - 5 = 23°
(3x) = 3(28) = 84°
Therefore, the angle measures of the two unknown angles are 23° and 84°.