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Firlakuza [10]
3 years ago
14

Two secants go through point A, which is a point in the exterior of a circle, makes a 32° angle. The measure of the bigger arc,

which those secants intercept, is 100°. Find the measure of the smaller arc.
Mathematics
1 answer:
MArishka [77]3 years ago
8 0

Answer:

The measure of the smaller arc is 36\°

Step-by-step explanation:

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

Let

x-----> the measure of the bigger arc

y----> the measure of the smaller arc

we know that

32\°=\frac{1}{2}(arc\ x-arc\ y)

we have

arc\ x=100\°

substitute the values and solve for arc y

32\°=\frac{1}{2}(100\°-arc\ y)

64\°=(100\°-arc\ y)

arc\ y=100\°-64\°=36\°

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