Q. 1314.2( 6 Votes )

In ∆PQR, if 3P = 4Q = 6R, calculate the angles of the triangle.

Answer :


Given: 3P = 4Q = 6R


Formula Used/Theory:-


Angle sum property


Sum of all angles of triangle is 180°


Solutions:-


If 3P = 4Q = 6R


Taking LCM of 3,4,6


We get 12


Then;


Dividing LCM by magnitude of each angle gives ratio of all 3 angles


P = 12/3 = 4


Q = 12/4 = 3


R = 12/6 = 2


Means angles are in ratio 4:3:2


Then;


Let all 3 angles of triangle be 4x;3x;2x


By angle sum property


4x + 3x + 2x = 180°


9x = 180°


x = = 20°


The angles of triangle will be 4×20°;3×20°;2×20°


The angles of triangle are 80°;60°;40°


Result:- The angles of triangle are 80°;60°;40°


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