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# I need help with these two questions and can you please explain how you got the answer?

### 1 Answer

- AlanLv 76 months agoFavorite Answer
Exterior Angle Rule

<ex angle = 1/2( outer arc - inner arc)

therefore

if arc are measured clockwise

<Angle A= 1/2 ( arc BC (from B to C) - arc RS (from S to R) )

36 = 1/2 ( arc BC - (1/4) arc BC) =

36= 1/2 BC - 1/8 BC = BC(4/8 -1/8) = (3/8) Arc BC

multiply both sides by 8/3

36*(8/3) = arc BC

arc BC = 96

arc RS = 96/4= 24 degrees

checking

36= (1/2)(96-24) = 1/2 (72) =36

37.

so AB is the side of a triangle with sides PA and PB.

All sides of equal.

Meaning it is an equilateral triangle

<P = 60 degrees (if you measured the shorter angle)

which would be 360-60 =300 degrees if you measure the other way.

alternatively

chord length formula

C = 2r*sin(theta/2)

so if r = C,

C/2C = sin(theta/2)

1/2 = sin(theta/2)

arcsin(1/2) = 30 or 150 = theta/2

theta = 2*30 or 2*150 = 60 or 300

again if you measure only the shorter angle = 60 degrees.

if you measure the wider angle it is 300 degrees.

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