9514 1404 393
Answer:
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°
