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Two angles are said to be supplementary if the sum of the measures of their angles is 180 degrees. If one angle is 30 degrees less than six times the other, what is the measure of the larger angle?

$$150^{\circ}$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:00

Two angles are complementa…

00:52

One angle measures $6^{\ci…

03:17

Two angles are said to be …

03:08

Two angles are supplementa…

01:47

01:32

Supplementary angles are a…

01:29

for the following problem. We have two angles that are supplementary to each other are trying to figure out the angle off the bigger one. So two angles are supplementary if they add up 280 degrees. So we'll be using linear equations to solve this problem and their linear because the unknown value is raised to the power of one. And we have to remember that addition and subtraction under each other, multiplication and division also under each other. So we have a plus B equals 180 degrees and were given the following information. Basically, one of the angles is 30 degrees, less than 60 other. So if one angle is equal to 30 degrees less than 60 other, this means it's six times bigger than the other one, less than 30 or a minus 30. So one of the angles is gonna go to this six times B minus 30 and now we can solve for angle beat by simply replacing a with this value right here. Six times B, minus 30 and 12 Original A plus Beatles 180 degrees. So we'll replace that. We're gonna have six times be, and it's 30 plus speak. 180 degrees. So now we'll just add up the piece that seven times be and it's pretty equals 100. And now we're gonna try toe. We arranged this to isolate seven B, so we're gonna have to add 30 to both sides of the equation. Yeah, and now we're gonna have 17 speed and then the thirties cancel out and we're left with 100 and 80 plus 30 is 210. Now we're going to divide both sides of the equation by seven in order to isolate it. Yeah, So B is going to equal to 210 divided by seven, which is just 30 degrees. So this is our smaller angle because it's less than half off the 180 degrees. So if since it's less than 90 it's a smaller angle. And again, we're looking for two angles, small angle and a big angle. This is a small one, so we could plug this back to the original question. A plus B equals 180 degrees. Ever gonna have eight is only north your ankle plus 30 which is our smaller angle. Both 180 degrees, you know, will simply just subtract 30 from both sides of the equation to get our larger value eight 180 minutes 30. This is simply 150 degrees. Oh, a people to 150 degrees. This is the angle off the larger one.

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