Question

The ratio of the measures of the three angles of a triangle is 4:5:9. Find the measure of the largest angle of the triangle.

Answer 1

`90^(\circ)`

Explanation:

The interior angles of all triangles sum up to
`180^(\circ)`. Therefore, we can write the following equation:

`4x+5x+9x=180`, where
`x` is some constant.

Combining like terms, we have
`18x=180,\: x=10`.

Therefore, the angles of this triangle are
`4(10)=40^(\circ), \: 5(10)=50^(\circ), \: 9(10)=90^(\circ)`, the largest of them being
`\fbox{$90^(\circ)$}`.