Advertisements
Advertisements
प्रश्न
Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.
Advertisements
उत्तर
\[\text{ Sum of the interior angles of the polygon }= \left( n - 2 \right)\pi\]
Number of sides in the pentagon = 5
\[ \therefore \text{ Sum of the interior angles of the pentagon }= \left( 5 - 2 \right)\pi = 3\pi\]
\[\text{ Each angle of the pentagon }= \frac{\text{Sum of the interior angles of the polygon}}{\text{Number of sides}} = \frac{3\pi}{5}\text{ rad }\]
\[\text{ Each angle of the pentagon }= \left( \frac{3\pi}{5} \times \frac{180}{\pi} \right)^\circ= 108^\circ\]
APPEARS IN
संबंधित प्रश्न
Find the radian measure corresponding to the following degree measure:
– 47° 30'
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`)
-4
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
10 cm
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:
\[\left( \frac{18\pi}{5} \right)\]
Find the degree measure corresponding to the following radian measure:
(−3)c
Find the degree measure corresponding to the following radian measure:
1c
Find the radian measure corresponding to the following degree measure:
300°
Find the radian measure corresponding to the following degree measure: 35°
Find the radian measure corresponding to the following degree measure: 7° 30'
Find the radian measure corresponding to the following degree measure: 125° 30'
The difference between the two acute angles of a right-angled triangle is \[\frac{2\pi}{5}\] radians. Express the angles in degrees.
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.
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.
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?
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.
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.
If the angles of a triangle are in A.P., then the measures of one of the angles in radians is
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\] radian at the centre is
A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
“The inequality `2^sintheta + 2^costheta ≥ 2^(1/sqrt(2))` holds for all real values of θ”
State whether the statement is True or False? Also give justification.
`cos (2pi)/15 cos (4pi)/15 cos (8pi)/15 cos (16pi)/15 = 1/16`
State whether the statement is True or False? Also give justification.
One value of θ which satisfies the equation sin4θ - 2sin2θ - 1 lies between 0 and 2π.
