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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