Question

Question-19 Find The Third Angle or Triangle Whose Two Angles Are 120
And 50°​

Answer 1

$\large\sf\underline{Given\::}$

• First angle = 120°

• Second angle = 50°

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$\large\sf\underline{To\:find\::}$

• The third angle

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$\large\sf\underline{Assumption\::}$

• Let the third angle be x .

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$\large\sf\underline{Concept\::}$

We know according to angle sum property of triangle :

★ $\bf\color{maroon}{Sum\:of\:angles\:in\:a\:triangle\:=\:180°}$

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$\large\sf\underline{Solution\::}$

Let's use the angle sum property here and frame an equation :

$\sf\:First\:angle\:+\:Second\:angle\:+\:Third\:angle\:=180°$

• Substituting the values we are given and the assumed value

$\sf\twoheadrightarrow\:120°\:+\:50°\:+\:x\:=180°$

• Proceeding with simple calculation

$\sf\twoheadrightarrow\:170°\:+\:x\:=180°$

• Transposing +170° to other side it becomes -170°

$\sf\twoheadrightarrow\:x\:=180°-170°$

$\sf\twoheadrightarrow\:x\:=10°$

$\small{\underline{\boxed{\mathrm\red{\twoheadrightarrow\:Third\:angle\:=\:10°}}}}$ $\sf{\maltese}$

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$\large\sf\underline{Verifying\::}$

So how would we check whether we got correct answer or not !?

Yeah we would again verify our answer using angle sum property. If we got the sum of all the angles we got as 180° our answers would be correct. Let's check :D

• Using angle sum property of triangle :

$\sf\leadsto\:120°+50°+10°=180°$

$\sf\leadsto\:170°+10°=180°$

$\sf\leadsto\:180°=180°$

$\bf\leadsto\:LHS=RHS$

$\large{\mathfrak\blue{hence\:verified\:!!}}$

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!! Hope it helps !!