9514 1404 393
Answer:
1. ∠EDF = 104°
2. arc FG = 201°
3. ∠T = 60°
Step-by-step explanation:
There are a couple of angle relationships that are applicable to these problems.
- the angle where chords meet is half the sum of the measures of the intercepted arcs
- the angle where secants meet is half the difference of the measures of the intercepted arcs
The first of these applies to the first two problems.
1. ∠EDF = 1/2(arc EF + arc UG)
∠EDF = 1/2(147° +61°) = 1/2(208°)
∠EDF = 104°
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2. ∠FHG = 1/2(arc FG + arc ES)
128° = 1/2(arc FG +55°) . . . substitute given information
256° = arc FG +55° . . . . . . multiply by 2
201° = arc FG . . . . . . . . . subtract 55°
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3. For the purpose of this problem, a tangent is a special case of a secant in which both intersection points with the circle are the same point. The relation for secants still applies.
∠T = 1/2(arc FS -arc US)
∠T = 1/2(170° -50°) = 1/2(120°)
∠T = 60°
Answer:
153.94 cm²
Step-by-step explanation:
Area of circle = πr² = π(7)² = 49π = 153.94 cm²
6 times 1/5 (which is also 0.2) is greater than 1
Answer:
x = 4
y = 10
Step-by-step explanation:
29x - 3 + 15x + 7 = 180 (Linear Pair)
44x + 4 = 180
44x + 4 = 180 - 4
44x = 176
x = 4
29(4) - 3
116 - 3
113
13y - 17 = 113 (Alternate Exterior Angles Theorem)
13y - 17 + 17= 113 + 17
13y = 130
y = 10
Answer:
a= 52
Step-by-step explanation:
82 + (x+60) + (x+54) = 180
82 + 2x + 114 = 180
2x + 196 = 180
2x = -16
x = -8
plug in -8 in x +60
-8 + 60 = 52
a = 52
