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)
A. 16°
B. 52°
C. 128°
D. 120°
Since the sum of the measures of two adjacent angles on a straight line is always 180°, we can set up 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
Now we can find the measure of the second angle, which is given by 8x:
8 * 16 = 128
Therefore, the measure of the second angle is 128°.
The answer is C. 128°.
A right angle is formed by two adjacent angles with measures of (x)° and (x+30)°. What are the two angle measures?
(1 point)
70° and 25°
30° and 60°
75° and 105°
60° and 90°
A right angle measures 90°. So 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
Now we can find the measure of the two angles:
First angle: x = 30°
Second angle: x + 30 = 30 + 30 = 60°
Therefore, the two angle measures are 30° and 60°.
The answer is B. 30° and 60°.