Question

The smallest angle in a triangle is
1
3
as large as the largest angle. The third angle is twice the smallest angle. Find the three angles.

The measures of the angles from smallest to biggest are
°,
°, and
°.

Answer 1

First, lets assign a letter to each angle:

a = smallest angle

b = largest angle

c = 3rd angle

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The question tells us the following:

$smallest\: angle=\frac{1}{3}\, largest\: angle$

Therefore: $largest\: angle = 3 \times smallest\: angle$

We are also told:

$3rd\: angle=2\times smallest\: angle$

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Now lets form three equations by swapping out the angles with the correlating letter:

$a=\frac{1}{3}b$

$b=3a$

$c=2a$

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Remember, angles in a triangle add up to 180, so we can make another equation:

$a + b + c = 180$

Now substitute in the values in terms of a, for b and c - and then solve for a.  (to solve the equation, everything has to be in the same terms, which is a in this case):

$a + b + c = 180$

$a + 3a + 2a = 180$

$6a = 180$

$a = 30$

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Now that we know what a is, we can work out what b and c is, by substituting in the value of a into their equations:

Value for b:

$b=3a$

$b=3(30)$

$b=90$

Value for c:

$c=2a$

$c=2(30)$

$c=60$

_______________________________________

a = smallest angle

b = largest angle

c = 3rd angle

So:

30 = smallest angle

90 = largest angle

60 = 3rd angle

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Answers:

The measure of the angles from smallest to biggest are:

30°,

60°, and

90°

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Answer 2

x + 5x + 2x = 180    

8x = 180  

x = 22.5 degrees ( smallest angle),  Largest Angle = 112.5 degrees and the third angle = 45 degrees

Let's call the smallest angle x.  Then the largest angle is 5x and then the third angle is 2x since it is twice the smallest angle.  We know that the sum of all the angles in a triangle is 180 degrees.

Step-by-step explanation:

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