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
186° and 88°
186 degrees and 88 degrees
121° and 59°
121 degrees and 59 degrees
129° and 51°
129 degrees and 51 degrees
125° and 55°
To find the measures of the two angles that make up the straight line (180°), we can set up the equation:
(2x + 3) + (x - 6) = 180
Combine the like terms:
3x - 3 = 180
Add 3 to both sides of the equation:
3x = 183
Divide both sides by 3:
x = 61
Now we can find the measures of the angles:
Angle 1: (2x + 3) = (2 * 61 + 3) = 125°
Angle 2: (x - 6) = (61 - 6) = 55°
Therefore, the measures of the two angles that make up the straight line are 125° and 55°. The correct answer is:
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.(1 point)
Responses
23° and 84°
23 degrees and 84 degrees
28° and 79°
28 degrees and 79 degrees
20° and 87°
20 degrees and 87 degrees
32° and 75°
To find the angle measures of the two unknown angles, we can set up the equation:
(x - 5) + (3x) = 107
Combine the like terms:
4x - 5 = 107
Add 5 to both sides of the equation:
4x = 112
Divide both sides by 4:
x = 28
Now we can find the angle measures:
Angle 1: (x - 5) = (28 - 5) = 23°
Angle 2: (3x) = (3 * 28) = 84°
Therefore, the angle measures of the two unknown angles are 23° and 84°. The correct answer is:
23 degrees and 84 degrees.