In the diagram below, tangent AB¯¯¯¯¯¯¯¯AB¯ is perpendicular to diameter CD¯¯¯¯¯¯¯¯CD¯ at CC. EE is the intersection of BD¯¯¯¯¯¯¯¯BD¯ with the circle.
EF¯¯¯¯¯¯¯¯EF¯ is a diameter with AA, EE, OO, and FF all collinear. If the measure of ∠B∠B is 12∘12∘ more than the measure of ∠A∠A, what is the measure of ∠B∠B in degrees?
Let ∠A∠A have measure xx and ∠B∠B measure yy. Thus y−x=12y−x=12.
EF¯¯¯¯¯¯¯¯EF¯ is a diameter, so arcs ECˆEC^ and CFˆCF^ add up to 180∘180∘. Therefore,
CDˆ−CEˆ2180−(90+x)90−x=∠B=2y=2y.CD^−CE^2=∠B180−(90+x)=2y90−x=2y.Combined with y−x=12y−x=12 we can solve for x=22x=22 and y=34y=34. Thus ∠B∠B measures 34∘34∘.
The correct answer is: 34
Can someone please explain how to get 180 - (90 + x) = 2y?