Question

What is the measure of angle A if it intercepts two arcs, one with a measure of 87 degrees and the other with a measure of 33 degrees?

Answer 1

Solution:

To find the measure of A, we will apply the intersecting secant theorem for the angle formed outside the circle,

The formula is

$A=\frac{1}{2}(Bigger\text{ arc angle}-Smaller\text{ arc angle\rparen}$

Where

$\begin{gathered} Bigger\text{ arc angle}=87\degree \\ Smaller\text{ arc angle}=33\degree \end{gathered}$

Substitute into the formula above

$\begin{gathered} A=\frac{1}{2}(87\degree-33\degree)=\frac{1}{2}(54\degree)=27\degree \\ A=27\degree \end{gathered}$

Hence, the measure of angle A is 27°