Two angles are supplementary . The measure of the first angle is 36 less than three times the second angle . What are the angles .

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akannan's profile pic

Ashley Kannan | Middle School Teacher | (Level 3) Distinguished Educator

Posted on

In solving this particular equation, ensuring that your formula is set up properly is going to be critical.  In knowing that 2 angles are supplementary, you know that when both are added together, they have to equal 180 degrees.  Supplementary angles means angles that add to 180 degrees.  You know with these parameters that your equation cannot exceed these limits.  From here, configuring the solution becomes following the rules established.

You know that two angles are needed, and that one of them is 36 less than three times the second angle.  This means that my first angle is going to be 3x- 36 because I am looking at something that is three times (3x) and 36 degrees less (-36) than my second angle which we will represent as simply x.  My formula looks like this when all is said and done:

3x- 36 + x= 180

Add like terms and I have 4x with the -36.  The 180 on the other side does not change.

4x + 36= 180

Isolate for x, which means I add minus 36 to both sides.

4x= 144

Solve for x.

x= 36

This means that one of the angles is 36 degrees and the other one is 144 degrees. If I add them together to run the check, I get 180, the measurement of supplementary angles.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If the angles are supplementary, that means that their sum is of 180 degrees.

Let x be the first angle and y, the second angle.

x + y = 180 (1)

x = 3y - 36 (2)

We'll replace (2) in (1):

3y - 36 + y = 180

4y + 36 = 180

We'll divide by 4;

y + 9 = 45

y = 45 - 9

y = 36

The other angle is:

x = 180 - 36

x = 144

The measures of the angles x and y are: x = 144 and y = 36.

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