Question

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Question=} Show that the angles of an equilateral triangle are 60° each.​

Answer 1

$\huge\mathfrak\red{Heya \: Mate! ♡}$

$\huge\mathcal\orange{QuEsTiOn:-}$

Show that the angles of an equilateral triangle are 60° each.

$\huge\mathcal\green{AnSwEr:-}$

$\bf{Theorem:}$

ᴀʟʟ ᴛʜᴇ ᴀɴɢʟᴇs ᴀɴᴅ sɪᴅᴇs ᴏғ ᴀɴ ᴇϙᴜɪʟᴀᴛᴇʀᴀʟ ᴛʀɪᴀɴɢʟᴇ ᴀʀᴇ ᴇϙᴜᴀʟ.

So, if they are equal, let the angles be (There are three interior angles in a Δ) = x, x, x

Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ϙᴜᴇsᴛɪᴏɴ :-

Sum of all the interior angles of a Δ = 180°

Therefore,

x + x + x = 180°

3x = 180°

$x = \frac{180°}{3}$

$x = 60°$

•°•, All the angles of a Δ measure 60°.

Answer 2

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$\longrightarrow$ Angles of an equilateral traingle are 60°

What is an equilateral triangle ?

$\implies$ A traingle whose all sides are equal.

• The sums of all the angles of a triangle are equal to 180°

[ Let the angles of the equilateral triangle be x ]

$\implies$ x + x + x = 180°

$\implies$ 3x = 180°

$\implies$ x = 180/3

$\implies$ x = 60°

Thus, proved that each angle of an equilateral triangle is equal to 60°

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