Question

the four angles of a quadrilaterals in the radio
1:2:3:4, find the measure of each angle of the Quardrilater?​

Answer 1

Given :

The four angles of a quadrilateral in the radio  1:2:3:4

To Find :

Measure of each angle of the quadrilateral

Solution :

Let angles be x , 2x , 3x , 4x respectively

We know that , " Sum of angles in a quadrilateral is 360° "

⇒ x + 2x + 3x + 4x = 360

⇒ 10x = 360

⇒ x = 36°  $\purple{\bigstar}$

→  x = 36° ←

→  2x = 2(36) = 72°  ←

→  3x = 3(36) = 108°  ←

→  4x = 4(36) = 144°  ←

More Info :

• Sum of angles in a straight line is 180°
• Sum of angles in a triangle is 180°

Answer 2

GIVEN :-

• Tʜᴇ ғᴏᴜʀ ᴀɴɢʟᴇs ᴏғ ᴀ ǫᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ɪs ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ $\bf\red{1\::\:2\::\:3\::\:4\:}$ .

TO FIND :-

• Tʜᴇ ᴍᴇᴀsᴜʀᴇ ᴏғ ᴇᴀᴄʜ ᴀɴɢʟᴇ ᴏғ ᴛʜᴇ ǫᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ .

SOLUTION :-

ʟᴇᴛ,

• Tʜᴇ ғᴏᴜʀ ᴀɴɢʟᴇs ᴏғ ᴛʜᴇ ǫᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ᴀʀᴇ,

1. $\bf\red{X}$
2. $\bf\red{2X}$
3. $\bf\red{3X}$
4. $\bf\red{4X}$

ᴡᴇ ʜᴀᴠᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

$\red\checkmark\:\bf\purple{Sum\:of\:angles\:of\:a\:quadrilateral\:=\:360^{\degree}\:}$

➳ X + 2X + 3X + 4X = 360°

➳ 10X = 360°

➳ X = 360/10

➳ X = 36°

$\huge\red\therefore$ The four angles of the quadrilateral are,

1. $\bf\pink{X}$ = 36°
2. $\bf\pink{2X}$ = 2 × 36° = 72°
3. $\bf\pink{3X}$ = 3 × 36° = 108°
4. $\bf\pink{4X}$ = 4 × 36° = 144°