Question

The measure of angles of a triangle are in the ratio 5:7:8.Find the measures.​

Answer 1

Given :

• Measure of three angles of a triangle are in the ratio 5:7:8 .

To Find :

• Measure of all three angles .

Solution :

As we know that Sum of all angles of a triangle is 180° . So ,

$\longmapsto\tt{5x+7x+8x=180^{\circ}}$

$\longmapsto\tt{20x=180^{\circ}}$

$\longmapsto\tt{x=\cancel\dfrac{180}{20}}$

$\longmapsto\tt\bf{x=9}$

Value of x is 9 ..

Therefore :

$\longmapsto\tt{Measure\:of\:1st\:Angle=5(9)}$

$\longmapsto\tt\bf{45^{\circ}}$

$\longmapsto\tt{Measure\:of\:2nd\:Angle=7(9)}$

$\longmapsto\tt\bf{63^{\circ}}$

$\longmapsto\tt{Measure\:of\:3rd\:Angle=8(9)}$

$\longmapsto\tt\bf{72^{\circ}}$

_______________________

VERIFICATION :

$\longmapsto\tt{5x+7x+8x=180^{\circ}}$

$\longmapsto\tt{5(9)+7(9)+8(9)=180^{\circ}}$

$\longmapsto\tt{45^{\circ}+63^{\circ}+72^{\circ}=180^{\circ}}$

$\longmapsto\tt\bf{180^{\circ}=180^{\circ}}$

HENCE VERIFIED

Answer 2

☆ɢɪᴠᴇɴ:

◕ ᴛʜᴇ ᴍᴇᴀsᴜʀᴇ ᴏғ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ 5:7:8.

☆ᴛᴏ ғɪɴᴅ:

◕ ᴍᴇᴀsᴜʀᴇs ᴏғ ᴀʟʟ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ.

☆sᴏʟᴜᴛɪᴏɴ:

ʟᴇᴛ x ʙᴇ ᴛʜᴇ ᴄᴏᴍᴍᴏɴ ᴍᴜʟᴛɪᴘʟᴇ ʜᴇʀᴇ.

ᴛʜᴇʀᴇғᴏʀᴇ ,

5x+7x+8x=180°.......[sᴜᴍ ᴏғ ᴀʟʟ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ɪs °]

: . 20x=180°

: . x=180/20

: . x=9

ᴛʜᴇʀᴇғᴏʀᴇ,

◆ᴛʜᴇ ᴍᴇᴀsᴜʀᴇ ᴏғ ᴛʜᴇ ғɪʀsᴛ

ᴀɴɢʟᴇ=5x=5×9=45°

◆ᴛʜᴇ ᴍᴇᴀsᴜʀᴇ ᴏғ ᴛʜᴇ sᴇᴄᴏɴᴅ ᴀɴɢʟᴇ=7x=7×9=63°

◆ᴛʜᴇ ᴍᴇᴀsᴜʀᴇ ᴏғ ᴛʜᴇ sᴇᴄᴏɴᴅ ᴀɴɢʟᴇ=8x=8×9=72

@ɪᴛᴢᴢsᴛʏʟɪsʜɢɪʀʟ♡