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प्रश्न
In a triangle, the sum of two angles is equal to the third angle. If the difference between these two angles is 20°, determine all the angles.
उत्तर
Let the two angles of a triangle be x and y respectively.
Then, the 3rd angle will be 180° - (x + y).
According to given information, we have
x + y = 180° - (x + y)
⇒ 2(x + y) = 180°
⇒ x + y = 90° ....(i)
And,
x + y = 20° ....(ii)
Adding eqns. (i) and (ii), we have
2x = 110°
⇒ x = 55°
⇒ 55° + y = 90°
⇒ y = 35°
⇒ 3rd angle
= 180° - (55° + 35°)
= 180° - 90°
= 90°
Hence, the three angles of a triangle are 55°, 35° and 90°.
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