Question

The angles of a quadrilateral are in the ratio 3:4:5:6

What is the difference between the largest and smallest angle?
(show working out)​

Answer 1

`60`

Explanation:

`Let\ the\ constant\ of\ proportionality\ between\ the\ angles\ be\ x\\Hence,\\\angle 1=3x\\\angle 2=4x\\\angle 3=5x\\\angle 4=6x\\Hence,\\We\ know\ through\ the\ Angle\ Sum\ Property\ Of\ A\ Quadrilateral\ that\ \\'The\ Sum\ Of\ All\ The\ Interior\ Angles\ Of\ A\ Quadrilateral\ is\ 360'.\\Hence,\\\angle 1+\angle 2+\angle 3+\angle4=360\\Hence,\\3x+4x+5x+6x=360\\7x+11x=360\\18x=360\\x=360/18\\x=20\\Now,\\From\ the\ observations\ we\ know\ that,\\`

`\angle4\ with\ a\ measure\ of\ 6x\ is\ the\ largest\ angle.\\While, \angle1\ with\ a\ measure\ of\ 3x\ is\ the\ smallest.\\Hence,\\6x-3x\\=3x\\As\ x=20,\\3x=3*20=60`