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

In a regular decagon, each interior angle measures (n-2) x 180° / n, where n is the number of sides of the polygon. 
For a decagon, each interior angle measures (10-2) x 180° / 10 = 144°.
Since the radius TBX8811 is perpendicular to the chord QR, the angle mTBX is half of the angle mQRX (as the two angles intercept the same arc).
Therefore, m 11ebfb55_24b3_ffbc_9d86_710bb4575452_TBX8811_11 = 1/2 * (180° - 144°) = 18°.
Since angle RXQ measures 144° (as explained above), angle TXQ measures 180° - 144° = 36°. Thus, angle TXB (which is supplementary to angle TXQ) measures 144°. Therefore, angle TBX (which is half of angle 11ebfb55_24b3_ffbc_9d86_710bb4575452_TBX8811_11) measures 18°, and so the correct answer is choice C, 72°.

In Regular Decagon QRSTUVWXYZ , Is a Radius