Ex 3.7, 5 (Optional) - In ABC, angle C = 3 B = 2 (A + B) - teachoo

Ex 3.7, 5 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Ex 3.7, 5 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3 Ex 3.7, 5 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 5 In a Δ ABC, ∠ C = 3 ∠ B = 2 (∠ A + ∠ B). Find the three angles. Let ∠A = x & ∠B = y Given that ∠C = 3 ∠B ∠ C = 3y Also, ∠ C = 2 (∠A + ∠B) ∠C = 2 (x + y) For ∠C = 3y Put ∠A = x ∠B = y and ∠C = 3y Since ABC is a triangle, By Angle Sum property ∠A + ∠B + ∠C = 180 x + y + 3y = 180 x + 4y = 180 For ∠C = 2(x + y) Put ∠A = x ∠B = y and ∠C = 2 (x + y) Since ABC is a triangle, By Angle Sum Property ∠A + ∠B + ∠C = 180 x + y + 2 (x + y) = 180 x + y + 2x + 2y = 180 3x + 3y = 180 3(x + y) = 180 (x + y) = 180/3 x + y = 60 Hence, the equations are x + 4y = 180 …(1) x + y = 60 …(2) From equation (1) x + 4y = 180 x = 180 − 4y Put x = 180 − 4y in equation (2) x + y = 60 180 − 4y + y = 60 180 − 60 = 4y − y 120 = 3y 3y = 120 y = 120/3 y = 40 Put y = 40° in equation (1) x + 4y = 180 x + (4 × 40) = 180 x + 160 = 180 x = 20 Thus, ∠ A = x = 20° ∠ B = y = 40° ∠C = 3y = 3 × 40 = 120°

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.