Question

In triangle ABC, angle B : angle C is 2 : 5 and angle A = 540

. Find angle B and angle C. Identify the type of triangle.​

Answer 1

Answer:

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Answer 2

${\huge{\rm{\underline{\underline{\rm{Question :-}}}}}}$

→ In triangle ABC, angle B : angle C is 2 : 5 and angle A = 54°

 

. Find angle B and angle C. Identify the type of triangle.​

${\huge{\rm{\underline{\underline{\rm{Solution :-}}}}}}$

→ Angles of Δ ABC

 ∠A  = 54° ( Given )

 ∠B = 2x

 ∠C = 5x

( taken according to the given ratios )

→ As we know that , sum of all angles of a triangle is 180°

  → ∠A + ∠B + ∠C = 180°

  → 54° + 2x° + 5x° = 180°

  → 54° + 7x° = 180°

  → 7x = 180° - 54°

  → 7x = 126°

  →  $x = \frac{126}{7} = 18$

  ∴ x = 18 °

_________

→ Now , the angles of Δ ABC are :-

 ∠ A = 54°

 ∠ B = 36°

 ∠ C = 90°

As , one angle is of 90° , the Δ ABC is right-angled triangle