Question

If mZ8 = 23°, find the measure of each missing angle. Give your reasoning.

A) mZ1 =
B) m2 =
C) m23 =
D) m24 =
E) m25 =
F) m26 =
G) m27 =

Answer 1

A) mZ1 = 157°

B) mZ2 = 23°

C) mZ23 = 157°

D) mZ24 = 23°

E) mZ25 = 157°

F) mZ26 = 23°

G) mZ27 = 157°

Step-by-step explanation:

In a circle, the sum of the central angles is always 360°. Since mZ8 = 23°, we can find the missing angles by subtracting mZ8 from 360° and dividing the result by 2.

A) mZ1 = 360° - mZ8/2 = 360° - 23°/2 = 157°

Similarly, for the consecutive angles, we can alternate between subtracting and adding mZ8 to find the measures.

B) mZ2 = mZ8 = 23°

C) mZ23 = 360° - mZ8 = 360° - 23° = 157°

D) mZ24 = mZ8 = 23°

E) mZ25 = 360° - mZ8 = 360° - 23° = 157°

F) mZ26 = mZ8 = 23°

G) mZ27 = 360° - mZ8 = 360° - 23° = 157°

In summary, the alternating pattern of subtracting and adding mZ8 allows us to efficiently find the measures of the missing angles in the circle.