A triangle has two corners of angles #(pi )/4# and #(5 pi)/12 #. What are the complement and supplement of the third corner?

Question

A triangle has two corners of angles #(pi )/4# and #(5  pi)/12  #.  What are the complement and supplement of the third corner?

Autumn Armstrong · Accepted Answer

#pi/6" and " (2pi)/3# The sum of the 3 angles of a triangle#=pi# hence 3rd angle#=pi-(pi/4+(5pi)/12)# and#pi/4=pi/4xx3/3=(3pi)/12" equivalent fractions "# #rArr"3rd angle "=pi-((3pi)/12+(5pi)/12)=pi-(8pi)/12# and#(8pi)/12" simplifies to" (2pi)/3# #rArr"3rd angle"=pi-(2pi)/3=(3pi)/3-(2pi)/3=pi/3# #"-------------------------------------------------------------"# 2 angles are#color(blue)" complementary""when they add up to"pi/2# #rArr"complement of"pi/3=pi/2-pi/3=(3pi)/6-(2pi)/6=pi/6# 2 angles are#color(red)"supplementary""when they add up to "pi# #rArr"supplement of"pi/3=pi-pi/3=(3pi)/3-pi/3=(2pi)/3#

Aaliyah Anderson · Answer

undefined The sum of the angles in a triangle is always π radians (180 degrees).

Given angles (π/4) and (5π/12), the third angle can be found by subtracting the sum of the known angles from π:

Third angle = π - [(π/4) + (5π/12)] = π - (π/4) - (5π/12) = π - (3π/4) - (5π/12) = π - (9π/12) - (5π/12) = π - (14π/12) = (12π/12) - (14π/12) = -π/12 radians.

The complement of the third angle is π/2 - (-π/12) = π/2 + π/12 = (6π/12) + (π/12) = 7π/12 radians.

The supplement of the third angle is π - (-π/12) = π + π/12 = (12π/12) + (π/12) = 13π/12 radians.