Question

Can somebody teach me inscribed angles! My 40 question summarize on circles in geometry is today and I need help on everything! ​

Answer 1

Inscribed angles are pretty easy, they're always half the corresponding central angle.  The arc measure are always of central angles.

1. We're told to arc is 62 degrees so the inscribed angle is half,

WXY = 31 degrees.

2. Here we're told the inscribed angle is 113 degrees so the arc is double,

DGF=226 degrees

3. Angles which subtend a diameter are always right angles.

PQR = 90 degrees

4. If we draw DC we see it's a radius too, so DC=DB and we have an isosceles triangle so DCB=47 degrees so BDC=180-47-47=86.  The central angle is the arc measure so

BC=86 degrees

5. Angle JNK=53 degrees and angles NJK=NKJ because we have an isosceles triangle, two sides radii.  So NKJ=(180-53)/2.

Similarly NKL=(180-65)/2

So angle JKL=NKJ+NKL=180 - (65+53)/2 = 180 - 118/2 = 121 degrees

I better leave the rest for you.