Question

3. Consider circle K on the right, where mZSKA= 74º.

740
Determine mzNTS.
A 370
B 74°
C 53°
D 106°

Answer 1

C

Explanation:

Angle AKS subtends Arc AS in the center of the circle. It will be the same measure as the Arc. If it were to subtend on the opposite end of the circle, the measure would have been HALF.

So, we can say:

Arc AS = 74

Now, Arc AN is half of the circle, so its measure is 180 degrees.

Since Arc AS is 74, we can say:

Arc SN + Arc AS = 180

Arc SN + 74 = 180

Arc SN = 106

Now,

Angle NTS subtends Arc SN to the opposite side of the circle, so its measure will be HALF of Arc SN. Hence:

∠NTS = 0.5 * 106

∠NTS = 53°

Answer choice C is right