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Verizon [17]
3 years ago
7

Find the measures of the angles formed by​ (a) two consecutive radii and​ (b) a radius and a side of a regular dodecagon.

Mathematics
1 answer:
IgorLugansk [536]3 years ago
8 0
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>°

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