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

The measure of the smaller arc is
`36\°`

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\°=(1)/(2)(arc\ x-arc\ y)`

we have

`arc\ x=100\°`

substitute the values and solve for arc y

`32\°=(1)/(2)(100\°-arc\ y)`

`64\°=(100\°-arc\ y)`

`arc\ y=100\°-64\°=36\°`