Question

PLEASE HELP DETAILS ARE BELOW I WILL RATE BRAINIEST CHORD AND ARCS FIND THE MEASURE OF ARC CD DETAILS BELOW

Answer 1

Wouldn’t it be 36.7 because that’s the arch am I right?

Answer 2

Answer:

The measure of arc CD is 114.6°.

Step-by-step explanation:

Let the center of the circle be O and OP is perpendicular to CD at point point P.

The perpendicular line from the center of circle divide each chord in two equal parts. so, CP=DP.

$CP=\frac{CD}{2}=\frac{36.7}{2}=18.35$

In a right angles triangle,

$\sin\theta =\frac{opposite}{hypotenuse}$

In a right angles triangle OPC,

$\sin\angle POC =\frac{18.35}{21.8}$

$\angle POC =\sin^{-1} (\frac{18.35}{21.8})$

$\angle POC \approx 57.3$

In triangle OPC and OPD,

$OC=OD$                  (Radius)

$OP=OP$                  (Reflexive property)

$CP=DP$                   (Altitude on chord from center)

By SSS postulate

$\triangle OPC\cong \triangle OPD$

$\angle POC\cong \angle POD$                      (CPCTC)

$\angle POC=\angle POD$

The measure of angle COD is

$\angle COD=\angle POC+\angle POD$

$\angle COD=2\angle POC$

$\angle COD=2(57.3)$

$\angle COD=114.6$

Therefore the measure of arc CD is 114.6°.