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Question:
If the measure of arc CB is units, what is the measure of ∠CAB?
Answer:
120°
Step-by-step explanation:
The figure has been attached to this response.
The figure shows a circle centered at A and has a radius of 4 units.
Also, the length of the arc CB (as given in the question) is units.
The length <em>L </em>of an arc is given by;
L = -----------------(i)
Where;
β = angle subtended by the arc at the center of the circle and measured in degrees
r = radius of the circle
From the question;
β = ∠CAB
r = 4 units
L =
<em>Substitute these values into equation (i) as follows;</em>
=
=> =
<em>Cancel 8</em><em> on both sides</em>
=
<em>Cross multiply</em>
3 x β = 360 x 1
3β = 360
<em>Divide both sides by 3</em>
<em /><em />
β = 120°
Therefore, the measure of ∠CAB is 120°
