Advertisements
Advertisements
प्रश्न
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Advertisements
उत्तर
\[\text{ Sum of the interior angles of the polygon }= \left( n - 2 \right)\pi\]
Number of sides in the octagon = 8
\[ \therefore \text{ Sum of the interior angles of the octagon }= \left( 8 - 2 \right)\pi = 6\pi\]
\[\text{ Each angle of the octagon }= \frac{\text{Sum of the interior angles of the polygon }}{\text{ Number of sides }} = \frac{6\pi}{8} = \frac{3\pi}{4}\text{ rad }\]
\[\text{ Each angle of octagon }= \left( \frac{3\pi}{4} \times \frac{180}{\pi} \right)^\circ= 135^\circ\]
APPEARS IN
संबंधित प्रश्न
Find the radian measure corresponding to the following degree measure:
25°
Find the radian measure corresponding to the following degree measure:
240°
Find the radian measure corresponding to the following degree measure:
520°
Find the degree measure corresponding to the following radian measure `(use pi = 22/7)`
`11/16`
Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)
`(5pi)/3`
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
21 cm
Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]
Find the degree measure corresponding to the following radian measure:
\[- \frac{5\pi}{6}\]
Find the degree measure corresponding to the following radian measure:
(−3)c
Find the degree measure corresponding to the following radian measure:
11c
Find the radian measure corresponding to the following degree measure: 135°
Find the radian measure corresponding to the following degree measure: 7° 30'
Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.
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 =
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.
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.
The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
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.
A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
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.
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?
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.
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
Find the value of `sqrt(3)` cosec 20° – sec 20°
If tan θ = `(-4)/3`, then sin θ is ______.
“The inequality `2^sintheta + 2^costheta ≥ 2^(1/sqrt(2))` holds for all real values of θ”
The value of tan1° tan2° tan3° ... tan89° is ______.
Which of the following is correct?
[Hint: 1 radian = `180^circ/pi = 57^circ30^'` approx]
State whether the statement is True or False? Also give justification.
The equality sinA + sin2A + sin3A = 3 holds for some real value of A.
