Question

The ratio of measurement of 1 : 2 : 3 is 4 : 9 : 5. Of the three angles, find the measurements of the largest.

Answer 1

The answer Is 90 degrees

Answer 2

Given:

The ratio of the three angles is 4:9:5.

To find the largest angle:

Let the first, second, and third angles be,

`\begin{gathered} \angle1=4x \\ \angle2=9x \\ \angle3=5x \end{gathered}`

Using the angle sum property of a triangle we get,

`\begin{gathered} \angle1+\angle2+\angle3=180 \\ 4x+9x+5x=180 \\ 18x=180 \\ x=10 \end{gathered}`

So, the largest angle is,

`\begin{gathered} 9x=9*10 \\ =90 \end{gathered}`

Hence, the measurement of the largest angle is 90 degrees.