Question

If two equal angles of an isosceles triangle measure 400 each, find the third angle

Answer 1

$\large\underline{\underline{{\pmb{\rm{\:Appropriate \:Question :-}}}}}$

Two angles of an isosceles triangle are are 40° . Find the third angle.

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$\large\underline{\underline{{\pmb{\rm{\: Given:-}}}}}$

• ➮ Two angles = 40°

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$\large\underline{\underline{{\pmb{\rm{\: To \: Find:-}}}}}$

• ➮ 3rd angle .

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$\large\underline{\underline{{\pmb{\rm{\:Solution :-}}}}}$

As we know :

$\large{\blue{\dag}}{\underline{\boxed{\red{\sf{Sum \: of \: angles{\small_{(Triangle)}} = 180°}}}}}{\blue{\dag}}$

3rd Angle :

$\: \: \: \: \large\twoheadrightarrow{\sf{ \: \: ∠1 + ∠2 + ∠3 = 180°}}$

$\: \: \: \: {\large\twoheadrightarrow{\sf{ \: \: 40° + 40° + ∠3 = 180°}}}$

$\: \: \: \: {\large\twoheadrightarrow{\sf{ \: \: 80° + ∠3 = 180°}}}$

$\: \: \: \: {\large\twoheadrightarrow{\sf{ \: \: ∠3 = 180° - 80°}}}$

$\: \: \: \: \: \: \: \: \: \: \: \purple{\bigstar}{\underline{\boxed{\green{\sf{ ∠3 = 100° }}}}}{\purple{\bigstar}}$

Hence :

$\large\color{cyan}{\underline{\blue{\underline{\orange{\rm{∠3 \: is \: 100° .}}}}}}$

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Verification :

$\leadsto{\sf{ ∠1 + ∠2 + ∠3 = 180°}}$

$\leadsto{\sf{40° + 40° + ∠3 = 180°}}$

$\leadsto{\sf{80° +100° = 180°}}$

$\leadsto{\sf{ 180° = 180°}}$

$\leadsto{\sf{ LHS = RHS}}$

Verified .

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Answer 2

Answer:

LET THIRD ANGEL=X

SUM OF ANGELS=180

<1+<2+<3=180

40+40+<3=180

<3=180-80

<3=100