Question

one angle of a traingle is equal to the dum of the remaining anes . if the ratio of the measures of the remaining two angles is 2:1 , find the measures of the three angles of the triangle .​

Answer 1

Given:-

• The ratio of 2nd and third angles = 2:1

• The sum of one angle of a triangle = Sum of other two angles

To Find :-

• The measurement of all angles of the Triangle.

Solution :-

We are given with the ratio of 2nd and third angles of a Triangle and also stated that the sum of all. the two angles = Measurement of one angle.

• Let the 2nd angle be 2x and third be x

• The sum of 2nd and third angle = 1st angle

• 2x+x = 1 st angle

• 3x = 1st angle

By Angle Sum Property of a Triangle

• x+2x+3x = 180°

• 6x = 180°

• x = 30

Hence the value of x = 30

Putting the value of x in 2x and 3x

★First angle = 3*x = 90°

★Second angle = 2*x = 60°

★Third angle = x = 30°

Verification :-

Angle Sum of a Triangle = 180°

The sum of angles = 90+60+30 = 180°

=> 180 = 180

Hence Varified

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