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3 years ago

Please solve!!!!!!!!! Thanks!

Mathematics

1 answer:

Nat2105 [25]3 years ago

4 0

Answer:

a) 60°
b) 80°
c) 100°
d) 50°
e) 30°

Step-by-step explanation:

The key here is that AB ║ EC. This makes arc AE have the same measure as arc BC. Since those have the same measure as AB and the three arcs together make a semicircle, each has measure 180°/3 = 60°.

Then the various arc measures are:

AB = 60°
BC = 60°
CD = 80° (given)
DE = 100° . . . . . since CDE is 180°
EA = 60°

Then your answers are ...

a) AE = 60°

b) ∠ABD = (1/2)(DE +EA) = (1/2)(100° +60°) = 80°

c) ∠DFC = (1/2)(CD +EB) = (1/2)(80° + (60° +60°)) = 100°

d) ∠P = (1/2)(DA -AB) = (1/2)(100° +60° -60°) = 50°

e) ∠PAB = (1/2)(AB) = (1/2)(60°) = 30°

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