Question

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.

Answer 1

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

$32\°=\frac{1}{2}(100\°-arc\ y)$

$64\°=(100\°-arc\ y)$

$arc\ y=100\°-64\°=36\°$