Question

Angles of a quadrilateral are in the ratio 1: 2: 3: 4. Find all angles. What special name can you give to this quadrilateral and why?​

Answer 1

Answer:

So here the angles will be x=36∘, 2x=72∘, 3x=108∘, and 4x=144∘. So the adjacent pair of angles is 180 degrees. So this is a trapezium as the sum of the adjacent angles on the parallel sides is 180 degrees. Note: Trapezium is a kind of quadrilateral.

Answer 2

Step-by-step explanation:

${\Huge{\underline{\underline{\bf{\maltese Question:-}}}}}$

$\mathrm{Angles\ of\ a\ quadrilateral\ are\ in\ the\ ratio\ 1:\ 2:\ 3:\ 4.\ Find\ all\ angles.\ What\ special\ name\ can\ you\ give\ to\ this\ quadrilateral\ and\ why?}$

${\Large{\underline{\underline{\bf{\maltese Let's\ Answer\ Your\ Question:-}}}}}$

:$\Rightarrow$ $\mathrm{Let\ the\ measure\ angle\ be\ x,\ 2x,\ 3x,\ and\ 4x}$

:$\Rightarrow$ $\mathrm{We\ know\ that\ the\ sum\ of\ measures\ of\ all\ four\ angles\ is\ 360⁰}$

:$\Rightarrow$ $\therefore$ $\mathrm{x\ +\ 2x\ +\ 3x\ +\ 4x\ =\ 360⁰}$

:$\Rightarrow$ $\mathrm{10x\ =\ 360⁰}$

:$\Rightarrow$ $\mathrm{x\ =\ 36⁰}$

:$\Rightarrow$ $\mathrm{2x\ =\ 2\ ×\ 36⁰\ =\ 72⁰}$

:$\Rightarrow$ $\mathrm{3x\ =\ 3\ ×\ 36⁰\ =\ 108⁰}$

:$\Rightarrow$ $\mathrm{4x\ =\ 4\ ×\ 36⁰\ =\ 144⁰}$

:$\Rightarrow$ $\mathrm{The\ measure\ of\ angles\ of\ quadilateral\ are\ 36⁰,\ 72⁰,\ 108⁰,\ and\ 144⁰.}$

:$\Rightarrow$ $\mathrm{We\ can\ see\ measure\ of\ all\ four\ angles\ are\ different.}$

:$\Rightarrow$ $\therefore$ $\mathrm{So\ the\ given\ quadilateral\ is\ trapezium.}$

${\Large{\underline{\underline{\bf{\maltese Hence,\ Solved \maltese}}}}}$