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

Raul Garrett · Accepted Answer

Step 1Let the angle be   θSupplement of angle   θ     is     180  −  θComplement of angle   θ     is     90  −  θStep 2Given that supplement is 11 times its complement  ⇒  (  180  −  θ  )  =  11  (  90  −  θ  )  ⇒  180  −  θ  =  990  −  11  θ  ⇒  −  θ  +  11  θ  =  990  −  180  ⇒  10  θ  =  810  ⇒  θ  =      810    10    ⇒  θ  =      81          ∘

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

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