1.

In a ΔABC, if 2∠A = 3∠B = 6∠C. Determine ∠A, ∠B and ∠C?

Answer»

DEGREE is not written in calculation.

Answer:

90° , 60° and 30°

Step-by-step explanation:

Here,

2∠A = 3∠B = 6∠C.

⇒ 2∠A = 3∠B   ;   2∠A = 6∠C

⇒ (2/3)∠A = B  ; (2/6)∠A = ∠C

⇒ (2/3)∠A = B  ;  (1/3)∠A = ∠C

   In a triangle :  

          Sum of all angles is 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A + (2/3)∠A + (1/3)∠A = 180

⇒ ( 3∠A + 2∠A +∠A ) / 3 =  180

⇒ 6∠A / 3 = 180

⇒ 2∠A = 180

⇒ ∠A = 180 / 2 = 90

           HENCE,

   ∠B = (2/3)∠A

         = (2/3) 90

         = 60

   ∠C = (1/3)∠A  

         = (1/3)90

         = 30

Hence the REQUIRED angles are 90° , 60° and 30°.

       ∠A = 90°  ; ∠B = 60° ; ∠C = 30°


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