One side of a triangle is produced and the exterior angle so formed is 140°. If the corresponding interior opposite angles are in the ratio 3:4, find the measure of all the angles of the triangle.

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Solution

Weknow that, Exterior angle = sum of opposite interior angles

given that ratio of interior angle = 3:4

required angles are 3x and 4x

that is 3x+4x = 140 according to given condition

solving this will gives

7x= 140

x =140/7

x= 20

therefore the angles are 320 and 420

that is 60 degree and 80 degree

now we want to find the third angle .

we know that the sum of the interior angles of a triangle = 180

third angle = 180-(sum of other 2 angles )

= 180-140 = 40 degree

therefore the angles are 40, 60 , 80 degrees

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