Answer:
- arc BF = 76°
- ∠M = 31°
- ∠BGE = 121°
- ∠MFB = 111°
Step-by-step explanation:
(a) ∠FBM is the complement of ∠FBC, so is ...
∠FBM = 90° -52° = 38°
The measure of arc BF is twice this angle, so is ...
arc BF = 2∠FBM = 2(38°)
arc BF = 76°
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(b) ∠M is half the difference between the measures of arcs BE and BF, so is ...
∠M = (1/2)(138° -76°) = 62°/2
∠M = 31°
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(c) arc FC is the supplement to arc BF, so has measure ...
arc FC = 180° -arc BF = 180° -76° = 104°
∠BGE is half the sum of arcs BE and FC, so is ...
∠BGE = (1/2)(arc BE +arc FC) = (138° +104°)/2
∠BGE = 121°
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(d) ∠MFB is the remaining angle in ∆MFB, so has measure ...
∠MFB = 180° -∠M -∠FBM = 180° -31° -38°
∠MFB = 111°
Answer:
x = 17
, y = 34
Step-by-step explanation:
Since the triangle is right use trig ratios to find x and y
note exact values sin30° =
, tan30° = 
sin30° =
= 
multiply both sides by y
y sin30° = 17 ( divide both sides by sin30° )
y =
= 34
tan30° =
= 
multiply both sides by x
x tan30° = 17 ( divide both sides by tan30° )
x =
= 17
Answer:
width = 19 inches
Step-by-step explanation:
Pythagorean theorem
23^2 = 13^2+x^2
529 = 169+x^2
x^2 = 360
x = 18.97