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Q. The angles of a triangle are in AP and the number of grades in the least is to the number of radians in the greatest as 40 is to π . Find the angle in degrees .
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➡Content Quality Needed⬅
Q. The angles of a triangle are in AP and the number of grades in the least is to the number of radians in the greatest as 40 is to π . Find the angle in degrees .
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Let a - d, a, a + d be the three angles of the triangle that form AP.
Given that the greatest angle is twice the least.
Now, 2(a - d) = a + d
2a - 2d = a + d
a = 3d ---------------(1)
Now by angle sum property,
(a - d) + a + (a + d) = 180°
3a = 180°
a = 60°----------------------(2)
from (1) and (2),
3d = 60°
d = 20°
Now, the angles are,
a - d = 60°- 20° = 40°
a = 60°
a + d = 60° + 20° = 80°.