Question

Suppose the largest angle of a triangle is the sum of the other two angles. Find the smallest angle of the
triangle if it is one 16th of the largest angle. Provide answer in decimal form.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Here we want to make a system of equations and solve it for the smallest angle of a triangle.

We will find that the smallest angle is 5.625°

First, let's define the variables:

a₁ = smallest angle

a₂ = middle angle

a₃ = largest angle.

We know that the sum of all interior angles of a triangle is equal to 180°, then we can write:

a₁ + a₂ + a₃ = 180°

We also know that:

"the largest angle of a triangle is the sum of the other two angles"

This can be written as:

a₃ = a₁ + a₂

And we know that:

"The smallest angle is one 16th of the largest angle"

Then:

$a_1 = \frac{a_3}{16}$

Writing together these 3 equations we get our system:

a₁ + a₂ + a₃ = 180°

a₃ = a₁ + a₂

$a_1 = \frac{a_3}{16}$

Now we want to solve this for a₁

To do it we need to replace equations into other equations.

How do we do this?

Notice that in the third equation we have:

a₃ = a₁ + a₂

Then we can replace it in the first equation:

a₁ + a₂ + a₃ = 180°

(a₁ + a₂) + a₃ = 180°

a₃ + a₃ = 180°

2a₃ =  180°

a₃ =  180°/2 = 90°

a₃ = 90°

Now we can use the last equation:

$a_1 = \frac{a_3}{16}$

To get the value of the smallest angle:

$a_1 = \frac{90 \°}{16} = 5.625 \°$

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