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.