Solve equations with adjacent angles Quick check:
Question 1: 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. A 128 B 120 C 52 D 16
Question 2: for two adjacent angles with measures x and (x+30) that make 90 degrees angle, what is x? A 60 B 30 C 15 D 20
Question 3: A right angle is formed by two adjacent angles with measures of x and (x+30) what are the two angle measures? A 30 and 60 B 70 and 25 C 75 and 105 D 60 and 90
Question 4: 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? A 121 and 59 B 125 and 55 C 186 and 88 D 129 and 51
Question 5: 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. A 32 and 75 B 28 and 79 C 23 and 84 D 20 and 87
Question 1: The measure of the second angle is (8x).
To find the value of x, set the two angles equal to each other:
5x - 28 = 8x
Solving for x, we get:
-28 = 3x
x = -28/3
Since it doesn't make sense to have a negative value for x in this context, we can conclude that this situation is not possible. Therefore, there is no correct answer choice for this question.
Question 2: The two angles will make a 90-degree angle, so their sum should be 90 degrees.
Setting up the equation:
x + (x + 30) = 90
Simplifying,
2x + 30 = 90
Subtracting 30 from both sides:
2x = 60
Dividing by 2:
x = 30
Therefore, the correct answer is B: 30.
Question 3: The two angles will make a right angle, so their sum should be 90 degrees.
Setting up the equation:
x + (x + 30) = 90
Simplifying,
2x + 30 = 90
Subtracting 30 from both sides:
2x = 60
Dividing by 2:
x = 30
Therefore, the two angle measures are 30 and 30 + 30 = 60. The correct answer is A: 30 and 60.
Question 4: The sum of the two angles that make up a straight line is 180 degrees.
Setting up the equation:
(2x + 3) + (x - 6) = 180
Simplifying,
3x - 3 = 180
Adding 3 to both sides:
3x = 183
Dividing by 3:
x = 61
Therefore, the two angle measures are 2(61) + 3 = 125 and 61 - 6 = 55. The correct answer is B: 125 and 55.
Question 5: The measure of the obtuse angle is 107 degrees, and the two adjacent angles have measures (x - 5) and (3x).
Setting up the equation:
(x - 5) + (3x) = 107
Simplifying,
4x - 5 = 107
Adding 5 to both sides:
4x = 112
Dividing by 4:
x = 28
Therefore, the two unknown angles are (28 - 5) = 23 and 3(28) = 84. The correct answer is C: 23 and 84.