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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