Question

The angles of a triangle are in the ratio 3:4:5. What is the measure of the smallest angle?

Answer 1

45 is the smallest angle in your triangle.

Explanation:

The sum of the interior angles of a triangle will be 180`°`.

Therefore, think of the ratios of 3:4:5 as variables followed by "x" (3x, 4x, and 5x).

Combine like terms and set the equation equal to 180, the amt. of degrees in a triangle:

123`x` = 180

Now, divide to isolate for `x`:

`(180/12)` = 15 , so `x` = 15

Now, substitute x for 15 in your variables:

3`x`, 4`x`, and 5`x`
3(15), 4(15), and 5(15)
45, 60, and 75 = 180

Therefore, 45 is the smallest angle.