A triangle has two corners of angles pi /12π12 and (7pi)/8 7π8. What are the complement and supplement of the third corner?

2 Answers
Feb 20, 2018

(11pi)/24" and "(23pi)/2411π24 and 23π24

Explanation:

"the third angle of the triangle is"the third angle of the triangle is

pi-(pi/12+(7pi)/8)=pi-(23pi)/24=pi/24π(π12+7π8)=π23π24=π24

• " complementary angles sum to "pi/2 complementary angles sum to π2

"complement of "pi/24=pi/2-pi/24=(12pi)/24-pi/24=(11pi)/24complement of π24=π2π24=12π24π24=11π24

• " supplementary angles sum to "pi supplementary angles sum to π

"supplement of "pi/24=pi-pi/24=(23pi)/24supplement of π24=ππ24=23π24

Feb 20, 2018

Complementary angle is (11pi)/2411π24

Supplementary angle is (23pi)/2423π24

Explanation:

All angles sum to piπ

Third angle is:

pi-(pi/12+(7pi)/8)π(π12+7π8)

pi-(23pi)/24=pi/24π23π24=π24

An angle and its complement add up to pi/2 π2

(pi)/24+theta=pi/2=>theta=(11pi)/24π24+θ=π2θ=11π24

An angle and its supplement add up to piπ

pi/24+theta=pi=>theta=pi-pi/24=(23pi)/24π24+θ=πθ=ππ24=23π24

:.

Complementary angle is (11pi)/2411π24

Supplementary angle is (23pi)/2423π24