A triangle has two corners of angles pi /12 and (5pi)/12 . What are the complement and supplement of the third corner?

1 Answer
Mar 2, 2018

Complement angle hatZ = pi/2, Supplement angle hatW = pi/2

Supplement angle W is also the exterior angle of the triangle.

Explanation:

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Given hat X= pi/ 12, hatY = (5pi)/12

Sum of the three angles of a triangle equals pi^c or 180^@

Hence hat Z = pi - pi/12 - (5pi)/12 = (pi /2)^c

Supplementary angle of hatZ is hatW

We know, hatZ + hatW = pi

Thus, hat W = pi - pi/2 = (pi/2)^c

Also in a triangle,

Exterior angle equals sum of the interior opposite angles.

:. hat W = hatX + hatY = pi/12 + (5pi)/12 = pi/2

Hence, verified.