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CBSE Class 10 Mathematics Question 29 of 29

Pair of Linear Equations in Two Variables — Question Ex 3.7 Q5

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Ex 3.7 Q5
Question

Ex 3.7 Class 10 Maths Question 5.
In a ∆ABC, ∠C = 3 ∠B = 2(∠A + ∠B). Find the three angles.

Answer

Let ∠A = x° and ∠B = y°.
Then ∠C = 3∠B = (3y)°.
Now ∠A + ∠B + ∠C = 180°
⇒ x + y + 3y = 180°
⇒ x + 4y = 180° …(i)
Also, ∠C = 2(∠A + ∠B)
⇒ 3y – 2(x + y)
⇒ 2x – y = 0° …(ii)
Multiplying (ii) by 4 and adding the result to equation (i), we get:
9x = 180°
⇒ x = 20°
Putting x = 20 in equation (i), we get:
20 + 4y = 180°
⇒ 4y = 160°
⇒  y =  \(\frac { 160 }{ 40 }\)  = 40°
∴ ∠A = 20°, ∠B = 40° and ∠C = 3 x 40° = 120°.

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CBSE Class 10 Pair of Linear Equations — Complete Guide

This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts

  • Unique solution: a1/a2 ≠ b1/b2 (intersecting lines)
  • Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
  • No solution: a1/a2 = b1/b2 ≠ c1/c2 (parallel lines)
  • Methods: Substitution, Elimination, Cross-multiplication
  • Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions

  1. Determine consistency of a system of equations
  2. Solve using elimination or substitution method
  3. Word problems: age, speed, fraction, geometry type
  4. Equations reducible to linear form (1/x, 1/y type)

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