## 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

Question

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

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Step-by-step explanation:

The triangle isosceles has two equal angles and two equal sides

The 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=36u00b0[/tex] ——> by central angle ( vertex angle of the isosceles triangle ABC)

Remember that

the sum of the internal angles of a triangle is equal to [tex]180u00b0[/tex]

so

[tex]m<CAB+m<DBC+m<ACB=180u00b0[/tex]

[tex]36u00b0+2m<DBC=180u00b0[/tex]

[tex]m<DBC=(180u00b0-36u00b0)/2=72u00b0[/tex]