Writing and Solving Equations

by Chuck

Find the measure of the largest angle of a triangle if it's 3 times as large as the smallest angle and the second angle is 20 degrees larger than the smallest angle. (The sum of the measures of the angles of a triangle is 180 degrees.)

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Dec 09, 2010
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by: Karin

Since all of the information is centered around the smallest angle, we are going to assign this as our variable.

Let the smallest angle = x (degrees)

The second angle is 20 degrees larger so this means: x + 20

The largest angle is 3 times as large as the smallest angle, so this means: 3x

Now we can add our three angles together and they must equal a total of 180 degrees.

x + (x+ 20) + 3x = 180

Step 1: Combine like terms

x + x + 3x + 20 = 180

5x + 20 = 180

Step 2: Subtract 20 from both sides.

5x + 20 -20 = 180 - 20

5x = 160

Step 3: Divide by 5 on both sides.

5x/5 = 160/5

x = 32 degrees.

If x is 32 degrees this means that the smallest angle is 32 degrees.

The 2nd angle is 32 + 20 = 52 degrees.

The largest angle is 3(32) = 96 degrees.

Check your answers:

32+52+96 = 180

I hope this helps,
Karin

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