Question

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

Answer 1

Heya!
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↪Let the two smaller angles be x and y respectively !


=> Now , according to the given question ->


=> Larger angle = 2 ( x + y ) ....................( 1 )


▪Applying the Angle Sum Property of a ∆ ,

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


=> 2x + 2y + x + y = 180


=> 3x + 3y = 180


-> Taking 3 common ,


=> 3 ( x + y = 60 )


=> Hence ( x + y ) = 60 . Put this value in Eq. (1)


=> Larger Angle = 2 ( x + y )

=> 2 ( 60 )


=> 120°


=> Smallest Angle = ¼ × 120 = 30°


=> Third Angle = 180 - ( 120 + 30 )

=> 180 - 150 = 30°



♦Hence the Angles are 30° , 30° and 120°

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Answer 2

Hey ❗

here's your answer ❗
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Let the other two angles be
${x}^{0} and \: {y}^{0}$

The largest angel = 2(x + y)

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

∴ (x + y) + x + y = 180°

⇒2x + 2y + x +y = 180

⇒ 3x + 3y = 180

⇒x + y = 60

∴ Form (1), the largest angel = 2(60°) = 120°

It is given that the smallest angel = 1/4 (largest angel)

∴ y = 1 /4 × 120° =30°

Putting y = 30 in (2), x + 30.

hence the angels are 30°, 30°, 120°
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@vaibhavhoax