Find the measure of angle whose supplement is four times its complement.Hint: Supplement and complement of an angle are ( 180 − θ ) ∘ and ( 90 − θ ) ∘ respectively

Question

Find the measure of angle whose supplement is four times its complement.Hint: Supplement and complement of an angle are   (  180  −  θ      )          ∘           and     (  90  −  θ      )          ∘       respectively

Dereon Parker · Accepted Answer

Step 1Let the angle be   θSupplement of angle   θ     is     180  −  θComplement of angle   θ     is     90  −  θStep 2Given that supplement is 4 times its complement  ⇒  (  180  −  θ  )  =  4  (  90  −  θ  )  ⇒  180  −  θ  =  360  −  4  θ  ⇒  −  θ  +  4  θ  =  360  −  180  ⇒  3  θ  =  180  ⇒  θ  =      180    3    ⇒  θ  =      60          ∘

Find the measure of angle whose supplement is four times its complement. Hint: Supplement and complement of an angles are (180-theta)^(circ) and (90-theta)^(circ) respectively.

Answered question

Answer & Explanation

New Questions in Pre-Algebra