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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