Q20 of 102 Page 49

In a triangle ∠A = x°, ∠B = 3x° and ∠C = y°. If 5x – 3y + 30 = 0 then prove that it is a right triangle.

Sum of interior angle of a triangle = 1800


x + 3x + y = 180


⇒ 4x + y = 180


⇒ y = 180 - 4x …equation (i)


5x - 3y + 30 = 0


Putting the value of y from equation (i) in above equation we get


5x - 3(180 - 4x) + 30 = 0


⇒ 5x - 540 + 12x + 30 = 0


⇒ 17x = 510


⇒ x = 300


Putting the value of x in equation (i) we get


y = 600


∠A = 300


∠ B = 900


∠ C = 600


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