Solve Equations with Adjacent Angles Quick Check
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Question
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)
Responses
128°
120°
16°
52°
To find the measure of the second angle, you need to set the two angle expressions equal to each other and solve for x.
So, (5x-28)° = (8x)°
To solve for x, you can subtract 5x from both sides of the equation:
-28° = 3x
Then, divide both sides of the equation by 3:
-28/3 = x
Now that you have the value of x, substitute it back into the expression for the second angle:
Second angle = 8x
Second angle = 8(-28/3)
Simplifying:
Second angle = -224/3
Therefore, the measure of the second angle is -224/3°.
None of the given options match this value, so there may be an error in the question or answer choices.
it has to be on of them
Apologies for the confusion. Let's solve the equation again:
(5x-28)° = (8x)°
Subtracting 8x from both sides:
-28° = 3x
Dividing both sides by 3:
-28/3 = x
Now substitute the value of x back into the expression for the second angle:
Second angle = 8x
Second angle = 8(-28/3)
Simplifying:
Second angle = -224/3
Converting to degrees:
Second angle = -74.67°
Since the options are in whole numbers, we can round the answer to the nearest whole number. Rounding -74.67° to the nearest whole number, we get -75°.
Therefore, the measure of the second angle is -75°.
However, none of the given options match this value, so again there may be an error in the question or answer choices.
pick from the answer list choices
Since none of the given options match the calculated measure of the second angle, it seems there may be an error in the question or answer choices. Unfortunately, I cannot choose an option from the given answer choices as none of them are correct based on the calculations. Please double-check the question and answer choices for accuracy.
For two adjacent angles with measures x° and (x+30)° that make up a 90° angle, what is x?(1 point)
Responses
20
60
15
30
To find the value of x, we can set up the equation based on the information given:
The sum of the measures of two adjacent angles forming a straight angle is 180°. Since they form a 90° angle, their sum would be half of that, which is 90°:
x° + (x+30)° = 90°
Combining like terms:
2x + 30 = 90
Subtracting 30 from both sides:
2x = 60
Dividing both sides by 2:
x = 30
Therefore, the value of x is 30.
Out of the given answer choices, the correct answer is 30.
A right angle is formed by two adjacent angles with measures of (x)° and (x+30)° . What are the two angle measures?(1 point)
Responses
60° and 90°
70° and 25°
75° and 105°
30° and 60°
To find the measures of the two angles, we need to set up the equation based on the given information:
The sum of the measures of two angles forming a right angle is 90°.
So, we have:
x° + (x+30)° = 90°
Combining like terms:
2x + 30 = 90
Subtracting 30 from both sides:
2x = 60
Dividing both sides by 2:
x = 30
Therefore, the measure of the first angle is 30°.
The measure of the second angle can be found by substituting the value of x:
Second angle = x + 30 = 30 + 30 = 60°
Therefore, the two angle measures are 30° and 60°.
Out of the given answer choices, the correct option is 30° and 60°.
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°