In circle A shown below, Segment BD is a diameter and the measure of Arc CB is 36°: Points B, C, D lie on Circle A; line segment BD is the diameter of circle A; measure of arc CB is 36 degrees. What is the measure of ∠DBC? 36, 72, 18, 54
Accepted Solution
A:
Answer:The answer is [tex]m<DBC=72\°[/tex]Step-by-step explanation:The triangle isosceles has two equal angles and two equal sidesThe triangle ABC is an isosceles triangle -----> see the attached figure[tex]AC=AB[/tex] -----> radius of the circle[tex]m<DBC=m<ACB[/tex] ------> angles of the base of the isosceles triangle ABC[tex]m<CAB=36\°[/tex] ------> by central angle ( vertex angle of the isosceles triangle ABC)Remember thatthe sum of the internal angles of a triangle is equal to [tex]180\°[/tex]so[tex]m<CAB+m<DBC+m<ACB=180\°[/tex][tex]36\°+2m<DBC=180\°[/tex][tex]m<DBC=(180\°-36\°)/2=72\°[/tex]