Someone please help me with 16-18 please it’s due in 30 mins

9514 1404 393

  16.  134°

  17.  20°

  18.  94°

Step-by-step explanation:

An inscribed angle is half the measure of the arc it intercepts.

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16. Arc QT is twice the measure of inscribed angle QST, given as 67°.

  Arc QT = 2×67°

  Arc QT = 134°

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17. Angle STR is half the measure of arc SR, so is ...

  m∠STR = (arc SR)/2 = 40°/2

  m∠STR = 20°

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18.  Arc RST is a semicircle, so has a measure of 180°. Then arc ST is the difference between that and arc RS:

  arc ST = 180° -40° = 140°

Angle RST subtends a semicircle, so is 180°/2 = 90°. We know angle QST is 67°, so the remaining portion, angle QSR must be the complement of that:

  m∠QSR = 90° -67° = 23°

Arc RQ will be twice this measure, or 46°.

So, the desired difference is ...

  mST -mRQ = 140° -46° = 94°

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47