Question

A triangular playground has angles with measures in the ratio 8 : 6 : 4. What is the measure of the smallest angle?

Answer 1

let's recall that the sum of all interior angles in a triangle is 180°.

we know the angles are in a 8:6:4 ratio, so we simply divide 180 by (8+6+4) and then distribute accordingly.

`\bf 8:6:4\qquad \qquad \left( 8\cdot \cfrac{180}{8+6+4} \right) : \left( 6\cdot \cfrac{180}{8+6+4} \right) : \left( 4\cdot \cfrac{180}{8+6+4} \right) \\\\\\ (8\cdot 10):(6\cdot 10):(4\cdot 10)\implies 80~:~60~:~\stackrel{\textit{smallest}}{40}`

Answer 2

20°

Explanation:

One way of doing this is to find the constant of proportionality, k:

8k + 6k + 4k = 90° Then 18k = 90°, and k turns out to be 90/18, or 5.

Then the angles are 8(5), 6(5) and 4(5). The smallest of these angles is thus 20°