"Sapphire Island is open 7 days a week. The park has 8 ticket booths, and each booth has a ticket seller from 10:00 am to 5 pm.
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Answer:
< CFE = 40°
Step-by-step explanation:
To better understand the solution, see attachment for the diagram.
Given:
BC parallel to DE
Measure of Arc BD = 58°
Measure of Arc DE = 142°
First step: Draw a diameter that passes through the centre of the circle and name it. In this case, the diameter is line ST.
The line ST divides the arc BD and arc DE into half.
That is:
Arc SC = 1/2(arc BC) =1/2(58)
Arc SC = 29°
Arc TE = 1/2(arc DE) =1/2(142)
Arc TE = 71°
Arc SC + Arc CE + Arc TE = 180° (Sum of angles in a semicircle
29° + Arc CE + 71° = 180°
Arc CE + 100° = 180°
Arc CE = 180-100
Arc CE = 80°
Inscribed angle = 1/2(intercepted angle)
<CFE = 1/2(Arc CE )
<CFE = 1/2(80)
< CFE = 40°
Given:
The recurring decimal is .
To prove:
Algebraically that the recurring decimal can be written as
.
Proof:
Let,
Multiply both sides by 100.
...(i)
Multiply both sides by 10.
...(ii)
Subtract (i) from (ii).
Divide both sides by 900.
So, .
Hence proved.