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### Course: MAP Recommended Practice>Unit 8

Lesson 4: Missing angle problems

# Equation practice with supplementary angles

Given the algebraic expressions that represent a pair of supplementary angles, Sal forms and solves an equation. Created by Sal Khan.

## Want to join the conversation?

• At Sal says, "And I'll assume it's in degrees." What other angle measurements are there, if any at all?
(12 votes)
• There are two other measures of a turn of a circle. There are radians, and there are gradians. 1 radian is equivalent to the ratio of the circle's circumference to its diameter, also known as 2*pi, and gradians is equal to the ratio of the circle's circumference to its diameter, divided by 400; therefore a gradian is equivalent to 1/400 of a turn in a circle, 9/10 of 1 degree, or pi/200 of a radian.
(18 votes)
• What is the difference between radians and degrees?
(8 votes)
• Radians are a different way to measure angles.
I always remember there are 2*pi radians in a circle, which is also equals 360 degrees
So, one radian = 360 degrees/(2*pi) = 57.3 degrees
You'll use radians quite a bit in trigoinometry
(5 votes)
• Lines AB and CD intersect at M. If the m∠AMD = 2x + 20 and the m∠DMB = 3x + 60, find the measure of ∠AMC.
(6 votes)
• I think I can figure your problem out. First, is your angle supplementary or complementary? If the angle is supplementary, the equation for x would be 2x+20+3x+60=180. If the angle is complementary, the equation would be 2x+20+3x+60=90. The answer for supplementary would be 60. The answer for complementary would be 24.

Hope this helped!
(0 votes)
• Accidentally used 90 degrees when solving it on my own and ended up with angle RPS = 5 degrees 😅 Make sure you use the right angle guys, and by 'right' I mean straight!!
(7 votes)
• How can we assume it forms a line based on how it looks? Shouldn't it be specified in the question?
(3 votes)
• I agree. I took geometry last year and the one thing that we had to "assume" sometimes was that a line was not two rays. Is that what you mean? I think that if the line is clearly straight then you can just assume that it is a line.

Hope this helps!!
(8 votes)
• hi sal, i want to tell you can you add missing numbers in equations
(6 votes)
• I'm told to determine the supplementary angle of a given edge with an improper fraction example 34 7/16 how do I go about that
(4 votes)
• While your use of "a given edge" does not make any sense with determining supplementary angles, if your angle has a fraction such as 7/16, you subtract 180 - 34 = 146, then borrow one from that, so 145 + 1 - 7/16 = 145 + 16/16 - 7/16 = 145 9/16 degrees.
(2 votes)
• How do you know if and angle is supplementary in a figure when it only has one found degree
(3 votes)
• Supplementary means all angles add up to 180, right? Which means, if you know one degree (one angle) and there are 2 angles, then you know that the other angle is 180 minus the angle you already know.

For example, lets say that one angle is 20. There are two angles with a sum of 180. Since ONE angle is 20, the other MUST be 160, because that is the only thing that adds up to 180.
Equation format: x + y = 180
x = First angle that you are trying to find
y = Second angle you are trying to find
These two numbers MUST equal 180.
(2 votes)
• i dont get it
(3 votes)
• What is a supplementary angle compared to a complimentary angle?
(0 votes)
• Complementary angles add up to 90 degrees. Graphically, if they were put together, they would form a right angle.
Supplementary angles add up to 180 degrees. Graphically, if they were put together, they would form a straight angle.
(8 votes)

## Video transcript

We're told that the measure of angle QPR-- so that's this angle right over here-- is 2x plus 122. And I'll assume that these are in degrees. So it's 2x plus 122 degrees. And the measure of angle RPS-- so that's this angle right over here-- is 2x plus 22 degrees. And they ask us to find the measure of angle RPS. So we need to figure out this right over here. So we would be able to figure that out if we just knew what x is. And lucky for us, we can use the information given to solve for x and then figure out what 2 times x plus 22 is. And the main big idea here, the thing that pops out here, is that the outside rays for both of these angle form a line. These two angles form a line. You could say that they are supplementary. Both of these angles are supplementary. 2x plus 22 plus another 2x plus 122 is going to add up to 180. We know that this entire angle right over here is 180 degrees. So we can say that the measure of angle QPR, this angle right over here, 2x plus 122, plus the green angle, plus angle RPS-- so plus 2x plus 22-- is going to be equal to 180 degrees. And now we can start simplifying this. We have two x's. We have another two x's. So those are going to add up to be 4x. And then we have 122 plus 22. So that's going to be 144. And the sum of those two are going to be equal to 180 degrees. We can subtract 144 from both sides. On the left-hand side, we're just going to be left with a 4x, this 4x right here. And on the right-hand side, we're going to have-- let's see, if we were subtracting 140, we would have 40 left. And then we have to subtract another 4, so it's going to be 36. Divide both sides by 4, and we get x is equal to 9. Now remember, we're not done yet. They didn't say solve for x. They said find the measure of angle RPS, which is 2 times x plus 22 or 2 times 9 plus 22, which is 18 plus 22, which is equal to 40. So the measure of angle RPS is 40 degrees.