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
121° and 59°
125° and 55°
129° and 51°
186° and 88°
To find the measures of the two angles that make up the straight line, we need to set up the equation 2x+3 + x-6 = 180 and solve for x.
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 back into the expressions for the angles, we find that the two angles are (2(61)+3)° = 125° and (61-6)° = 55°.
Therefore, the measures of the two angles that make up the straight line are 125° and 55°.
The correct answer is option: 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
20° and 87°
23° and 84°
32° and 75°
28° and 79°
To find the angle measures, we need to set up the equation (x-5) + (3x) = 107 and solve for x.
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 back into the expressions for the angles, we find that the two angles are (28-5)° = 23° and (3(28))° = 84°.
Therefore, the angle measures of the two unknown angles are 23° and 84°.
The correct answer is option: 23° and 84°