Question

prove sum of all angles of triangle is 180

Answer 1

HEY MATE HERE IS YOUR ANSWER

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We need to prove :- the sum of the angles of triangle is 180°.

Proof :-

↪️ let us see what is given in the statement about that is the hypothesis and what we need to prove we are given Triangle PQR and <1,<2 and <3 are the angles of triangle PQR.

we need to prove that <1 + <2 + <3 = 180° let is draw a line XP which parallel to QR through the opposite vertex P as shown in figure so that we can use the properties related to parallel lines.

$\bold {Now, XPY \: is \: a \: line}$

$\bold{Therefore,}$

$\bold {<4 + <1 + <5 = 180°------(1)}$

But XPY II QR and PQ, PR are transversal.

$\huge \bold {So,}$

<4 = <2 and <5 = <3 ( Alternate angles)

Substituting <4 and <5 in (1) we get,

<2 + <1 + <3 = 180°

That is,

$\underline {\bold {<1 + <2 + <3 = 180°}}$

$\huge \boxed {HENCE, PROVED}$

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Hope it will help you

$<marquee >$

$\huge {\boxed {\longrightarrow \: Thanks \: You \longleftarrow}}$

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Answer 2

Solutions :-


Q: Prove sum of all angles of triangle is 180.

=>
According to figure there is a ∆ABC.


To prove :- ∠ABC + ∠CAB + ∠ACB = 180°


Now,
Construction :- Through point A. Draw a line BC || EF


Proof :-
∠ABC = ∠DAB (Alternate Angles)
∠BCA = ∠EAC (Alternate Angles)
∠DAB + ∠BAC + ∠EAC = 180° (Linear Pair)



We get,
∠DAB = ∠ABC _______(i)
∠EAC = ∠BCA _______(ii)
∠DAB + ∠BAC + ∠EAC = 180° _______(iii)


Substitute the value of (i) and (ii) in (iii)

∠ABC + ∠BAC + ∠BCA = 180°


Hence,
Sum of all angles of triangle is 180.
Proved ✔✔