Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

Find the degree measure corresponding to the following radian measure: 
 1^c

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: −56°

Find the radian measure corresponding to the following degree measure: 135°

Find the radian measure corresponding to the following degree measure: −300°

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.

One angle of a triangle \[\frac{2}{3}\] x grades and another is \[\frac{3}{2}\] x degrees while the third is \[\frac{\pi x}{75}\] radians. Express all the angles in degrees.

Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.

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.

Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.

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