Q. 74.6( 23 Votes )

The sum of two angles of a triangle is 116° and their difference is 24°.Find the measure of each angle of the triangle.

Answer :

70°, 46°, 64°


Let P, Q and R are three angles of triangle PQR.


Now,


P + Q = 116° ___________________ (i)


P - Q = 24° ___________________ (i)


Adding equation (i) and (ii),


2 P = 140°


P = 70° ______________________ (iii)


Subtracting equation (i) and (ii),


2 Q = 92°


Q = 46° _______________________ (iv)


We know that sum of angles of triangle = 180°


P + Q + R = 180° [Sum of angles]


70° + 46° + R = 180° [From equation (iii) and (iv)]


R = 64°


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