Question

THREE ANGLES OF A TRIANGLE ARE IN THE RATIO 2:3:4 FIND ITS GREATEST ANGLE

Answer 1

Answer:

Given :-

• The three angles of a triangle are in the ratio of 2 : 3 : 4.

To Find :-

• What is greatest angles.

Solution :-

Let,

➲ First Angle = 2x

➲ Second Angle = 3x

➲ Third Angle = 4x

As we know that :

★ Sum Of All Angles Of Triangle = 180° ★

According to the question by using the formula we get,

⇒ 2x + 3x + 4x = 180°

⇒ 5x + 4x = 180°

⇒ 9x = 180°

⇒ x = 180°/9

⇒ x = 20°/1

➠ x = 20°

Hence, the required angles are :

❒ First Angle : of a triangle :

↦ First Angle = 2x

↦ First Angle = 2(20°)

↦ First Angle = 2 × 20°

➦ First Angle = 40°

❒ Second Angle of a triangle :

↦ Second Angle = 3x

↦ Second Angle = 3(20°)

↦ Second Angle = 3 × 20°

➦ Second Angle = 60°

❒ Third Angle of a triangle :

↦ Third Angle = 4x

↦ Third Angle = 4(20°)

↦ Third Angle = 4 × 20°

➦ Third Angle = 80°

∴ The greatest angles of a triangle is 80°.

Answer 2

$\huge \color{Indigo} {\mid{\fbox{\sf{Answer}}\mid}}$

_________________________________

$\bf \pink {\fbox {Given:-}}$

➻ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ ᴛʜʀᴇᴇ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ɪs 2:3:4

__________________________________

$\bf \purple {\fbox {Consideration:-}}$

➻ ʟᴇᴛ ᴜs ᴄᴏɴsɪᴅᴇʀ,

$➛{Angle\: 1=2x}$

$➛{Angle\:2=3x}$

$➛{Angle\: 3=4x}$

__________________________________

$\bf \orange {\fbox {we know:-}}$

➻ᴛʜᴇ sᴜᴍ ᴏғ ᴀʟʟ ᴀɴɢʟᴇs ɪɴ ᴀ ᴛʀᴀɪɴɢʟᴇ =180°

__________________________________

$\bf \red {\fbox {so,}}$

${Angle\:1+Angle\:2+\:Angle\:3=180°}$

$➛{2x+3x+4x=180°}$

$➛{9x=180°}$

$➛{x=\frac{180°}{9}}$

$\tt {\fbox {x=20°}}$

__________________________________

➻ ᴀs ᴡᴇ ɢᴏᴛ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ 'x' ᴡᴇ ᴄᴀɴ ᴅɪsᴄᴏᴠᴇʀ ᴛʜᴇ 3 ᴀɴɢʟᴇs ᴏғ ᴛʜᴇ ᴛʀᴀɪɴɢʟᴇ ᴛᴏ ɴᴏᴛɪᴄᴇ ɪᴛs ɢʀᴇᴀᴛᴇsᴛ ᴀɴɢʟᴇ

$➛{Angle\: 1=2(20°)}$

$➛{40°}$

$➛{Angle\: 2=3(20°)}$

$➛{60°}$

$➛{Angle\: 3=4(20°)}$

$➛{80°}$

__________________________________

$\bf \green {\fbox {Henceforth,}}$

➻ᴀɴɢʟᴇ 3 ,ɪ.ᴇ, 80° ɪs ᴛʜᴇ ɢʀᴇᴀᴛᴇsᴛ ᴀɴɢʟᴇ

__________________________________

$\bf \blue {\fbox {point\: to\: be\: noted:-}}$

☛ɴᴏᴡ,ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ᴛʜᴀᴛ ᴍᴀʏ ᴀʀɪsᴇ ᴡᴏᴜʟᴅ ʙᴇ ,ᴡʜʏ ᴛʜᴇ sᴜᴍ ᴏғ ᴀʟʟ ᴀɴɢʟᴇs ɪɴ ᴀ ᴛʀɪᴀɴɢʟᴇ ʙᴇ 180°?

➻Ⓡⓔⓐⓢⓞⓝ:-

☞ɪɴ ᴀ ᴛʀɪᴀɴɢʟᴇ,ᴏɴᴇ ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ ɪs ᴇǫᴜᴀʟ ᴛᴏ ᴛʜᴇ sᴜᴍ ᴏғ ᴛʜᴇ ᴏᴛʜᴇʀ ᴛᴡᴏ ᴀɴɢʟᴇs ɪɴ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ.

☞ɪɴ ᴏᴛʜᴇʀ ᴡᴏʀᴅs, ᴛʜᴇ ᴏᴛʜᴇʀ ᴛᴡᴏ ᴀɴɢʟᴇs ɪɴ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ (ᴛʜᴇ ᴏɴᴇs ᴛʜᴀᴛ ᴀᴅᴅ ᴜᴘ ᴛᴏ ғᴏʀᴍ ᴛʜᴇ ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ) ᴍᴜsᴛ ᴄᴏᴍʙɪɴᴇ ᴡɪᴛʜ ᴛʜᴇ ᴛʜɪʀᴅ ᴀɴɢʟᴇ ᴛᴏ ᴍᴀᴋᴇ ᴀ 180 ᴀɴɢʟᴇ.

__________________________________

$\color{Indigo} {\mid{\fbox{\sf{Hope\: it\: works}}\mid}}$