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
186° and 88°
186 degrees and 88 degrees
129° and 51°
129 degrees and 51 degrees
121° and 59°
To find the measures of the two angles that make up the straight line, we can set up the equation:
(2x + 3) + (x - 6) = 180
Combining like terms, we get:
3x - 3 = 180
Adding 3 to both sides, we get:
3x = 183
Dividing both sides by 3, we get:
x = 61
Substituting x = 61 back into the original equations, we get:
(2(61) + 3) = 125
(61 - 6) = 55
Therefore, the measures of the two angles that make up the straight line are 125° 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 the two unknown angles, we can set up the equation:
(x - 5) + (3x) = 107
Combining like terms, we get:
4x - 5 = 107
Adding 5 to both sides, we get:
4x = 112
Dividing both sides by 4, we get:
x = 28
Substituting x = 28 back into the original equations, we get:
(28 - 5) = 23
(3(28)) = 84
Therefore, the angle measures of the two unknown angles are 23° and 84°.