Question

three angles of the triangle are in AP if the commonest angle is 50 degree then find the other angles​​

Answer 1

Answer:

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Smallest angle = 50°let the difference be dthen other angle are 50°+d and 50°+2d∵sum of all angles of triangle = 180°⇒50°+(50°+d) +(50°+2d) = 180°⇒3d = 180° - 150° = 30°⇒d = 10°so others angles are 50°+10° = 60° and 50°+ 20° = 70°

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Answer 2

$\huge\underline\mathbb{ANSWER}$

The other angles measure 60° and 70°.

${\underline{\bf{\purple{GIVEN\: :-}}}}$

Commenest angle = 50°.

${\underline{\bf{\purple{To\:Find\::-}}}}$

Other Angles = ?

$\huge\underline\mathbb{SOLUTION}$

$\bf{Let\:the\:difference\:be\:d.}$

${\underline{\bf{\purple{Then\::-}}}}$

Other angles are 50°+ d and 50° + 2d.

$\bf{As\:we\:know\:that,}$

Sum of all angles of triangle is 180°.

$50 \degree+(50 + d)\degree+ (50 + 2d)\degree= 180 \degree\\ \\ 3d \degree=( 180 - 150 ) \degree\\ \\ 3d \degree = 30 \degree\\ \\ d \degree =(\cancel \frac{30}{3} ) \degree \\ \\ d \degree \: = 10 \degree$

${\underline{\bf{\purple{Therefore,}}}}$

Other angles are 50° + 10° = 60°

And, 50° + 20° = 70°.

${\underline{\bf{\purple{Verification\::}}}}$

$\bf{We\:know\:that,}$

Sum of all angles of triangle = 180°

So, ∠A + ∠B + ∠C = 180°

Substituting the values, we get,

50° + 60° + 70° = 180°

180° = 180°

L.H.S = R.H.S

$\bf{Hence,\:it\:is\:Verified.}$