Question

the measures of the angles of a triangle are in A.P. and the greatest is 5 times the smallest (least) . find the angles in degree and radian.​

Answer 1

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Let the angles of the triangle be (a – d) °, a° and (a + d) °.

We know that the sum of angles of triangle is 180°.

⇒ a – d + a + a + d = 180°

⇒ 3a = 180°

∴ a = 60°

Given greatest angle = 5 × least angle

Greatest angle

--------------------------- = 5

Least angle

a+d

--------- = 5

a-d

60+d

---------- =5

60-d

⇒ 60 + d = 300 – 5d

⇒ 6d = 240

∴ d = 40

Hence, angles are:

⇒ (a – d) ° = 60° – 40° = 20°

⇒ a° = 60°

⇒ (a + d) ° = 60° + 40° = 100°

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