Question

find the measures of the angles of each triangle. the ratio of the measures of the three angles is 7:5:8

Answer 1

The angles are 63°, 45° and 72°

Explanation:

We have the ratios and we know that the sum of all the internal angles within a triangle is equal to 180°.

Therefore, the measure of each angle will be equal to the ratio of each angle multiplied by 180, just like that

`\begin{gathered} A\text{\degree=}(a)/(a+b+c)\cdot180 \\ B\text{\degree=}(b)/(a+b+c)\cdot180 \\ C\text{\degree=}(c)/(a+b+c)\cdot180 \\ \text{where a = 7, b = 5 and c = 8} \end{gathered}`

Replacing in each case:

`\begin{gathered} A\text{\degree=}(7)/(7+5+8)\cdot180=63\text{\degree} \\ B\text{\degree=}(5)/(7+5+8)\cdot180=45\text{\degree} \\ C\text{\degree=}(8)/(7+5+8)\cdot180=72\text{\degree} \end{gathered}`