Question

प्र.13 एक त्रिभुज के कोण 2 : 3 : 4 के अनुपात में हैं, तो त्रिभुज के सभी कोण ज्ञात करो। ​

Answer 1

Answer:

Let Triangle ABC be the required triangle.

A:B:C = 2:3:4 - given

Let the common multiple be x.

:. angle BAC = 2x

angle ABC = 3x

angle ACB = 4x

In triangle ABC,

angle ABC + angle BAC + angle ACB = 180° - { sum of measures of all angles in a triangle is 180° }

:. 3x + 2x + 4x = 180°

:. 9x = 180°

:. x = 180°

9

:. x = 20°

Substituting the values,

angle BAC = 2x = 2(20) = 40°

angle ABC = 3x = 3(20) = 60°

angle ACB = 4x = 4(20) = 80°

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