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the largest angle of a triangle is equal to the sum of other two triangles. the smallest angle is 1/4 of the largest angle .find the angles of the triangle.

Note by Pooja Arora
4 years, 4 months ago

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Let largest angle be \(4x\)

then smallest angle = 1/4 of largest angle = \(x\)

Therefore, middle (or third) angle should be --> \(180 - (4x +x) = 180 - 5x\)

But the first statement says that sum of two angles = largest angle

=> \(x + (180 - 5x) = 4x\)

=> \(x = 22.5 ^ \circ\)

So the angles are --> \(90 ^ \circ , 67.5 ^ \circ , 22.5 ^ \circ\)

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Kishlaya Jaiswal - 4 years, 4 months ago

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thanx a lot...

Pooja Arora - 4 years, 4 months ago

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The first statement gives us that the largest angle is of \( 90^{\circ}\) The second statement gives us the smallest angle to be \(22.5^{\circ}\). So the angles are \( 90^{\circ}\), \(22.5^{\circ}\) , \(67.5^{\circ}\)

Vikram Waradpande - 4 years, 4 months ago

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thanku so much..

Pooja Arora - 4 years, 4 months ago

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Let the largest angle be \(4x\)

Then, it says that the smallest angle is \(\frac {1}{4}\) of the largest angle which would be \(x\)

So, the last angle would be \(4x-x=3x\)

Lets make it as \(4x+3x+x=180\Rightarrow8x=180\) So, \(x=22.5\), \(3x=67.5\), and \(4x=90\)

Timothy Wong - 4 years, 4 months ago

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