Question

In circle A shown below, line ED is a diameter and the measure of arc CB is 36°.



What is the measure of ∡DBC?

36°

72°

18°

54°

Answer 1

@Calcmathlete

Answer 2

First of all. Three theorems you need to know.
If a triangle is inscribed in a circle and the hypotenuse is the diameter, then the triangle is a right triangle.
If an angle is inscribed in a circle, then the angle is half the measure of it's intercepted arc.
A triangle's interior angles add up to 180.
Can you figure it out using that?

Answer 3

I know the theorems im still confused though

Answer 4

Alright. What type of triangle is CBD knowing the first theorem above?

Answer 5

That its a right triangle .

Answer 6

Alright. Angle CDB is an inscribed angle. It's intercepted arc is 36º. Using the second theorem, what is the measure of Angle CBD?

Answer 7

18?

Answer 8

Yup. FInally. Triangle CBD has two known angle measures, 90 and 18. Using the third theorem, what is the unknown measure? i.e. <DBC?

Answer 9

72?

Answer 10

\[\huge \text{YESSS!!!!!}\]

Answer 11

\[\tiny lol\]