Answer:
4: 264°; 5: 120°; 6: 54°; 7: 45°; 8: 87°; 9: 27°
9: x=200, y=100; 10: x=68; y=99
Step-by-step explanation:
The relations between angles and arcs in this problem set are ...
- The sum of central angles in a circle is 360°
- The measure of an arc is the measure of the central angle it subtends
- The measure of an inscribed angle is half the measure of the arc it subtends
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B.
3.
no identifier is given
4.
Arc DBC is the difference between a full circle (360°) and short arc DC. The measure of short arc DC is marked as 96°, so ...
arc DBC = 360° -96° = 264°
5.
Αrc BC is twice the measure of the inscribed angle BDC it subtends.
arc BC = 2×60° = 120°
6.
Arc AB is the difference between 360° and the sum of arcs AD, DC, and CB.
arc AB = 360° -(90° +96° +120°) = 54°
7.
Angle ACD is half the measure of arc AD.
Angle ACD = 90°/2 = 45°
8.
Angle ADC is half the measure of arc AC, which is the sum of arcs AB and BC
angle ADC = (54° +120°)/2 = 87°
9.
Angle ACB is half the measure of arc AB
angle ACB = 54°/2 = 27°
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C.
9.
x° is the arc whose central angle is 200°
x° = 200°
y° is half the measure of x°
y° = 200°/2 = 100°
10.
The relations between arcs and inscribed angles mean that opposite angles in an inscribed quadrilateral are supplementary.
x° = 180° -112° = 68°
y° = 180° -81° = 99°
