The five interior angles in a pentagon are in the ratio 2:3:4:5:6. What is the measure of the pentagon's largest angle?

Let All angles be x times multiplied to ratio, so we"ll get : -

2x + 3x + 4x + 5x + 6x = 540°

20x = 540

x = 540/20

⇒ x = 27,

so angles are : -

⇒ 2x = 2*27 = 54°

⇒ 3x = 3*27 = 81°

⇒ 4x = 4*27 = 108°

⇒ 5x = 5*27 = 135°

⇒ 6x = 6*27 = 162°

Hence 162° is the greatest angle