Question

Line BD is tangent to the circle at B and the measure of AC is 108 what is the measure of angle CBD

Answer 1

Answer:36

Explanation:

Answer 2

Concept,

Two chords with a shared termination point on the circle make an inscribed angle in a circle. The vertex of the angle is this shared terminal point. An inscribed angle is equal to half the length of the intercepted arc.

Given,

We have been given a figure in which the line
`BD` is the tangent to the circle at the point
`B` and the measure of the arc
`AC` is
`108^(\circ)}`. And also we have some options:

A.
`38^(\circ)}`

B.
`18^(\circ)}`

C.
`118^(\circ)}`

D.
`72^(\circ)}`

To find,

We have to choose the correct option which tells the measure of the angle of
`CBD`.

Solution,

In the figure, we can see that
`\angle ABC` is an inscribed angle and we know that the inscribed angle is half of the measure of the intercepted arc.

And from the figure arc
`AC` is the intercepted arc.

Thus, we can write

`\angle ABC=\frac{\widehat{AC}}{2}`

`\angle ABC=(108)/(2)`

`\angle ABC=54^(\circ)`

So, the measure of
`\angle ABC=54^(\circ)`.

Now given that
`BD` is a tangent to the circle at the point
`B`.

Thus, we will get

`\angle ABC+\angle CBD=90^(\circ)`

`54^(\circ)+\angle CBD=90^(\circ)`

`\angle CBD=90^(\circ)-54^(\circ)`

`\angle CBD=36^(\circ)`

Thus, the measure of the angle
`CBD=36^(\circ)`.

So, the correct option is A.
`36^(\circ)`.