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what is the measure of the indicated central angle?

a) 10 degrees

b) 15 degrees

c) 20 degrees

d) 25 degrees

e) none of the above

Explanation:

The radius of the circle is 24, so the circumference is

C = 2*pi*r

C = 2*pi*24

C = 48pi

The whole distance around the circle (perimeter) is exactly 48pi units

However, we only want 2pi of those units as the arc length shows

Divide 2pi over 48pi, and reduce

(2pi)/(48pi) = 1/24

So the arc shown is 1/24th of a full 360 degree revolution. Meaning we multiply the fraction 1/24 by 360 to get

(1/24)*360 = 360/24 = 15

The arc measure is 15 degrees which is equal to the measure of the central angle as well.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.