In regular decagon QRSTUVWXYZ, is a radius. Find m .
A) 45°
B) 60°
C) 72°
D) 144°

Question

In regular decagon QRSTUVWXYZ,  is a radius. Find m  .
A) 45° 
B) 60° 
C) 72° 
D) 144°

Quizplus · Accepted Answer

A regular decagon has 10 sides, so each interior angle measures:

(10-2) * 180° / 10 = 144°

Since the given segment is a radius, it divides the decagon into two congruent isosceles triangles. Each of these triangles has angles measuring:

(180° - 144°) / 2 = 18°

Adding this angle to the adjacent interior angle of the decagon gives:

144° + 18° = 162°

Since the angle we want is supplementary to this angle (they form a linear pair), we subtract from 180°:

180° - 162° = 18°

Therefore, m11eb4b36_76a2_30d3_a05a_ff4377780e84_TB7237_11 = 18°. However, since this is not one of the answer choices given, we must convert it to degrees that are listed. We notice that 18° is exactly one-eighth of the interior angle of the decagon:

144° / 8 = 18°

So we can express our answer as:

m11eb4b36_76a2_30d3_a05a_ff4377780e84_TB7237_11 = 1/8 * 144° = 18°

The closest answer choice to this value is C) 72°. To verify that this is indeed the best choice, we can check that 72° is exactly four times 18°, which makes sense since the given segment divides the decagon into four congruent triangles.

In Regular Decagon QRSTUVWXYZ, Is a Radius