Given:
The ratio of the three angles is 4:9:5.
To find the largest angle:
Let the first, second, and third angles be,
[tex]\begin{gathered} \angle1=4x \\ \angle2=9x \\ \angle3=5x \end{gathered}[/tex]Using the angle sum property of a triangle we get,
[tex]\begin{gathered} \angle1+\angle2+\angle3=180 \\ 4x+9x+5x=180 \\ 18x=180 \\ x=10 \end{gathered}[/tex]So, the largest angle is,
[tex]\begin{gathered} 9x=9\times10 \\ =90 \end{gathered}[/tex]Hence, the measurement of the largest angle is 90 degrees.
