Answer:
23 degrees
Step-by-step explanation:
We see that arc LM is 67 degrees. By definition, that means that the central angle <LPM also equals 67 degrees.
We also see that arc LMO is just a semicircle, which means that it is 180 degrees, by definition (because a whole circle is 360 degrees and a semicircle is just half a circle). In addition, angle MPN has that little square in its angle, which means that it is 90 degrees. By definition, its arc MN is also equal to 90 degrees. Then:
Arc LMO = arc LM + arc MN + arc ON
180 = 67 + 90 + arc ON
Solving, we get that arc ON = 180 - 67 - 90 = 23 degrees. By definition, that means the corresponding central angle <NPO is also equal to 23 degrees.
Notice that angles NPO and KPL are vertical angles, which means that by definition, they are equal in degree measure. So, since <NPO = 23, then <KPL = 23. Arc KL is the corresponding arc of <KPL, so by definition, arc KL is also 23 degrees.
Thus, the answer is 23 degrees.
Hope this helps!
