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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.

Respuesta :

calculista

Answer:

The measure of the smaller arc is [tex]36\°[/tex]

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

[tex]32\°=\frac{1}{2}(arc\ x-arc\ y)[/tex]

we have

[tex]arc\ x=100\°[/tex]

substitute the values and solve for arc y

[tex]32\°=\frac{1}{2}(100\°-arc\ y)[/tex]

[tex]64\°=(100\°-arc\ y)[/tex]

[tex]arc\ y=100\°-64\°=36\°[/tex]

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