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:

Angles are 36, 72, 108, and 144.

Name of the quadrilateral is trapezium.

Step-by-step explanation:

Let's say the angles are 1x, 2x, 3x, and 4x

Then,

=> x + 2x + 3x + 4x = 360

Solving for x

=> 10x = 360

=> x = 36

The angles are :-

• 1x = 36°
• 2x = 72°
• 3x = 108°
• 4x = 144°

Hence, we can call this a trapezium since all the angles are different.

Answer 2

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_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

$\tt{\longrightarrow {Let\ the\ measure\ angle\ be\ x,\ 2x,\ 3x,\ and\ 4x} }$

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

$\boxed{\therefore \tt{x\ +\ 2x\ +\ 3x\ +\ 4x\ =\ 360⁰}}$

$\tt \green{\longrightarrow10x\ =\ 360⁰}$

$\tt \green{ \longrightarrow \: x\ =\ 36⁰}$

$\tt \green{ \longrightarrow2x\ =\ 2\ ×\ 36⁰\ =\ 72⁰}$

$\tt \green{ \longrightarrow3x\ =\ 3\ ×\ 36⁰\ =\ 108⁰}$

$\tt \green{ \longrightarrow4x\ =\ 4\ ×\ 36⁰\ =\ 144⁰}$

$\huge\boxed{\tt\therefore\red{ 114°}}$

$\tt { \longrightarrow \: The\ measure\ of\ angles}$

$\tt{of\ quadilateral\ are\ 36⁰,\ 72⁰,\ 108⁰,\ and\ 144⁰.}$

$\tt{ \longrightarrow \: We\ can\ see\ measure\ of}$

ㅤ$\tt{all\ four\ angles\ are\ different.}$

$\boxed { \tt \: \therefore \: So\ the\ given\ quadilateral\ is\ trapezium.}$

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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