One of the most important and conceptual question from linear equations in two variables in which we have to find the angle of a triangle if it is given that in a △ABC,∠A=x, ∠B=(3x−2), ∠C=y. Also, ∠C−∠B=9.

Kindly give me a detailed solution of this question by using the properties of linear equations

RS Aggarwal, Class 10, chapter 3E, question no 52

## Ina△ABC, (By angle sum property)

∠A+∠B+∠C=180∘

∠C−∠B=9

⟹y−(3x−2)=9

∴y=7+3x

x+(3x−2)+y=180∘

⟹4x−2+7+3x=180∘

⟹x=25∘

∴y=7+3×25=82∘

∴∠A=x=25∘,B=3x−2=73∘

∠C=y=82∘