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Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
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Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.
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Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.
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Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are
Angles of the quadrilateral in radians =
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The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.
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The angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.
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The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
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The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.
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A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?
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Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.
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A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
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The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.
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A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
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Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.
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Find the diameter of the sun in km supposing that it subtends an angle of 32' at the eye of an observer. Given that the distance of the sun is 91 × 106 km.
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If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
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Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm.
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If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
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If the angles of a triangle are in A.P., then the measures of one of the angles in radians is
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The angle between the minute and hour hands of a clock at 8:30 is
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