CLASS-8
GEOMETRY-TRIANGLE- PROBLEM & SOLUTION

TRIANGLE- PROBLEM & SOLUTION


Example.1) In a ∆ ABC, if ∠A = 75⁰,  ∠B = 90⁰, then find ∠C = ?

Ans.)  In ∆ ABC, ∠A + ∠B + ∠C = 180⁰

So, as per the given condition - 

      ∠A + ∠B + ∠C = 180⁰

  Or,  75⁰ + 90⁰ + ∠C = 180⁰

  Or,  ∠C = 180⁰ - (75⁰ + 90⁰) =  180⁰ - 165⁰ =  15⁰      (Ans.)



Example.2) Prove that, each angle of an equilateral triangle is 60⁰

Ans.)  In the figure, XYZ in an equilateral angles

So, XY = YZ = ZX => ∠X = ∠Y = ∠Z

But, we know ∠X + ∠Y + ∠Z = 180⁰ 

  Or,   ∠X + ∠X + ∠X = 180⁰ 

  Or,     3 ∠X  =  180⁰

  Or,    ∠X  =  180⁰/3 = 60⁰

 Similarly,  ∠Y =  180⁰/3 = 60⁰

  Similarly,  ∠Z =  180⁰/3 = 60⁰

Hence,  ∠X  =  ∠Y  =  ∠Z  =  60⁰                  (Ans.)



Example.3) Find ∠BAC from the figure.


∠BCD => ∠BAC + ∠ABC = 125⁰

       => ∠BAC + 65⁰ = 125⁰

       => ∠BAC = 60⁰    (Ans.)