Find the measure of the arc or angle indicated assume that lines which appear tangent are tangent

Solution:

We know that the external angle is half the difference of the intercepted arcs.

From the figure 1

External angle = 161°

So the measure of the arc = (161 - 41)/ 2 = 120/2 = 60°

From the figure 2

Here the external angle can be found as

(x - 59)/ 2 = 31

x - 59 = 62

x = 62 + 59 = 121°

Therefore, the measure of angle is 60° and 121°.

Find the measure of the arc or angle indicated assume that lines which appear tangent are tangent

Summary:

The measure of the arc or angle indicated assuming that lines which appear tangent are 60° and 121°.