Find the measures of the angles formed by (a) two consecutive radii and (b) a radius and a side of a regular dodecagon.
1 answer:
See the picture to better understand the problem
we know that
A regular dodecagon has 12 sides
Central angle of a regular polygon is an angle whose vertex is the center of the polygon with two consecutive radii
thus
the measure of a central angle is
m∠AOC=360/n
where n is the number of sides
so
m∠AOC=360/12-----> 30°
therefore
the answer Part a) is
<span>the measure of the angle formed by two consecutive radii is 30 degrees
Part b)
we know that
OAC is an isosceles triangle
so
OA=OC
m</span>∠OAC=m∠OCA
<span>the sum of the internal angles of a triangle is 180 degrees
</span>so
180=2*m∠OAC+m∠AOC-----> m∠OAC=[180-30]/2----> 75°
the answer part b) is
<span>the measure of the angle formed by a radius and a side is 75</span>°
we know that
A regular dodecagon has 12 sides
Central angle of a regular polygon is an angle whose vertex is the center of the polygon with two consecutive radii
thus
the measure of a central angle is
m∠AOC=360/n
where n is the number of sides
so
m∠AOC=360/12-----> 30°
therefore
the answer Part a) is
<span>the measure of the angle formed by two consecutive radii is 30 degrees
Part b)
we know that
OAC is an isosceles triangle
so
OA=OC
m</span>∠OAC=m∠OCA
<span>the sum of the internal angles of a triangle is 180 degrees
</span>so
180=2*m∠OAC+m∠AOC-----> m∠OAC=[180-30]/2----> 75°
the answer part b) is
<span>the measure of the angle formed by a radius and a side is 75</span>°
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Answer:
Maureen earned $123.19 doing odd jobs
Step-by-step explanation:
The compound interest formula is given by:
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
In this question:
Compounded quarterly means that
10 years, so
9% interest, so
There is $300.00 in the account, which means that
How much did Maureen earn doing odd jobs?
This is P.
Maureen earned $123.19 doing odd jobs