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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Total number of marbles:
75 + 50 + 100 + 25 = 250
Probability of selecting a red marble:
25/250 (since 25 out of 250 marbles are red)
Since the top and bottom of this fraction are both divisible by 25, we can go ahead and divide them both by 25, simplifying to 1/10.
Probability of selecting a green marble:
50/250
Simplifies to 2/10
Simplifies to 1/5.
Probability of selecting a blue or orange marble
(75+100)/250
175/250
Simplifies to 7/10.
To find the probability that each event occurs in order, simply multiply them all together.
75 + 50 + 100 + 25 = 250
Probability of selecting a red marble:
25/250 (since 25 out of 250 marbles are red)
Since the top and bottom of this fraction are both divisible by 25, we can go ahead and divide them both by 25, simplifying to 1/10.
Probability of selecting a green marble:
50/250
Simplifies to 2/10
Simplifies to 1/5.
Probability of selecting a blue or orange marble
(75+100)/250
175/250
Simplifies to 7/10.
To find the probability that each event occurs in order, simply multiply them all together.