Question

Find the degree measure of the angle or the intercepted arc indicated in each figure

Answer 1

Let's solve point a of the question. To calculate the diameter of the figure we can solve it using the Pythagorean theorem

$\begin{gathered} NK=\sqrt{NL^2+KL^2} \\ NK=\sqrt{12^2+5^2} \\ NK=\sqrt{144+25} \\ NK=\sqrt{169} \\ NK=13 \end{gathered}$

Let us now calculate part b.

$mNLK=180$

Let us now calculate part c.

$mNJK=180$

Now let us calculate the arc for the part d. As it is a right triangle it would be:

$m\angle NLK=90$

Now let us calculate for part e

$mKL=45.2$

Finally, for part f

$\begin{gathered} mNL=180-45.2 \\ mNL=134.8 \end{gathered}$