Question

If the angles of a quadrilateral are in the ratio 3:4:5:6, then find the angles of the quadrilateral.

• A. ${60}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${120}^{\circ }$
• B. ${120}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$, ${60}^{\circ }$
• C. ${120}^{\circ }$, ${60}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$
• D. ${80}^{\circ }$, ${100}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${120}^{\circ }$

Given, the angles of the quadrilateral are in the ratio 3:4:5:6.

$\text{Let the angles be}3x,4x,5x,\text{and}6x.$

$\text{The sum of the angles of a quadrilateral}\text{is equal to}{360}^{\circ }.$

$\text{Therefore,}3x+4x+5x+6x={360}^{\circ }\Rightarrow 18x={360}^{\circ }\Rightarrow x=\frac{{360}^{\circ }}{18}\Rightarrow x={20}^{\circ }$

$\text{The angles are:}3x=3\times 20={60}^{\circ }4x=4\times 20={80}^{\circ }5x=5\times 20={100}^{\circ }6x=6\times 20={120}^{\circ }.$

$\text{Thus the angles are}{60}^{\circ },{80}^{\circ },{100}^{\circ }\text{and}{120}^{\circ }.$