Answer:
- B
- 152°
- B
- A
Explanation:
The measure of an arc is twice the measure of the inscribed angle that subtends that arc. A tangent is a special case where the chord that is one leg of the inscribed angle has a length of zero.
1. Short arc LJ is 2a°. Short arc LK is 2b°. Then arc JLK is 2(a+b)°, and short arc JK is ...
arc JK = 360° -2(a +b)° . . . . . matches choice B
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2. Long arc WY is twice the measure of "inscribed" angle WYZ, so is ...
long ard WY = 2(104°) = 208°
Then short arc WY is ...
arc WXY = 360° -208° = 152°
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3. The arc measures are double those of the corresponding inscribed angles. We can add up the arcs around the circle:
(arc AB +arc BC) = 2×70° = 140° . . . inscribed angle relation
(arc BC +arc CD) = 2×98° = 196° . . . inscribed angle relation
arc AB + arc BC +arc CD +arc DA = 360° . . . . sum around the circle
Adding the first two equations with arc DA, we have ...
(arc AB + arc BC) +(arc BC +arc CD) +arc DA = 360° +arc BC
140° +196° +80° = 360° +arc BC
416° -360° = arc BC = 56° . . . . . matches choice B
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4. Angle C and angle A are supplementary in this inscribed quadrilateral.
angle C = 180° -98° = 82° . . . . . matches choice A