Question

The largest angle of triangle is twice the sum of the other two. the smallest is one-fourth of the largest determine all the angles is degrees.

Answer 1

Hello here is your answer by Sujeet yaduvanshi



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Question:-The largest angle of triangle is twice the sum of the other two. the smallest is one-fourth of the largest determine all the angles is degree

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Solution::Let the smaller two angles be x and y

 

therefore, acc. to the question, 

largest angle of triangle = 2 (x+y) 

 

Now, as we know that,

Angle sum of a triangle = 180°

 

x + y + 2(x+ y) =  180°

x+y+2x+2y =  180°

3x+3y =  180°

x+y =  60°

 

thus, the largest angle =  60°

smallest angle =  60°/4 =  15°

and 

the other angle =  60° -  15° = 45° 

hence, the angles are 60° , 15°  and 45° .

Answer 2

Heya!!

here's your answer!!!

$let \: the \: other \: two \: angles \: be \: {x}^{0} and \: {y}^{0} ,$
where x ≥ y.

the largest angle = 2(x+y)

since the sum of the angles of a triangle = 180°

∴ 2(x+y) + x + y = 180° => 2x+ 2y + x + y = 180

3x +3y = 180 => x + y = 60

∴ from (1), the largest angle = 2(60°) = 120°

it is given that the smaller angle @ = 1/4(largest angle)

∴ y = 1/4×120° = 30°

putting y = 30 in (2), x+30 = 60 => x= 30.

hence the angle are 30°,30°,120°.

glad help you

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