Quadrilateral ABCD is inscribed in this circle.What is the measure of angle C?Enter your answer in the box.°
Accepted Solution
A:
Answer:[tex]m<C=62\°[/tex]Step-by-step explanation: we know thatIn an inscribed quadrilateral opposite angles are supplementarysoIn this problem[tex]m<D+m<B=180\°[/tex][tex]m<C+m<A=180\°[/tex]step 1Find the value of x[tex]m<D+m<B=180\°[/tex]substitute the values and solve for x[tex](x+20)\°+(3x)\°=180\°[/tex][tex]4x=180\°-20\°[/tex][tex]x=160\°/4=40\°[/tex]step 2Find the measure of angle A[tex]m<A=(2x+38)\°=2(40\°)+38\°=118\°[/tex]step 3Find the measure of angle C[tex]m<C+m<A=180\°[/tex]substitute the values and solve for m<C[tex]m<C+118\°=180\°[/tex][tex]m<C=180\°-118\°=62\°[/tex]