Question

The measures of the angles of PQR are in the ratio 2:5:5. What are the measures of the angles?

5-3 angles number 4

Answer 1

`30^circ`, `75^circ`, and `75^circ`

Explanation:

If the three angles are in the ratio `2:5:5` then their measures are `2x`, `5x`, and `5x`. The sum of the angles of a triangle is `180^circ`, so `2x+5x+5x=180^circ`.

`2x+5x+5x=180^circ`
`12x=180^circ`
`x=15^circ`

So the angles are `2(15^circ)`, `5(15^circ)`, and `5(15^circ)`, which simplify to `30^circ`, `75^circ`, and `75^circ`.