Name: Convert Degree Into Radian & Radian Into Degree
Uploaded: 2019-07-19
Duration: 7 min
Description: Let’s understand the concept of circular and radian measure of an angle. We will also learn how to convert degrees to radians and vice versa with the help of...

Question

One angle of a quadrilateral has measure

\frac{2 π^{c}}{5}

and the measures of other three angles are in the ratio

2 : 3 : 4 .

Find their measures in degree and radian.

Accepted Answer

One angle of a quadrilateral has measure $\frac{2 π^{c}}{5}$

We know that, $π^{c} = 180 °$

$\Rightarrow \frac{2 π^{c}}{5} = 180 \times \frac{2}{5}$

$∴ \frac{2 π^{c}}{5} = 72 °$

Now we are given that the measures of other three angles are ratio $2 : 3 : 4$

Let the ratio be $x$

So, the angles are $2 x, 3 x$ and $4 x$

Property: Sum of all angles of quadrilateral is $360 °$

So, $72 + 2 x + 3 x + 4 x = 360$

$\Rightarrow 72 + 9 x = 360$

$\Rightarrow 9 x = 288$

$\Rightarrow x = 32$

So, the angles are $2 x = 2 \times 32 = 64 °, 3 x = 3 \times 32 = 96 °$ and $4 x = 4 \times 32 = 128 °$

Therefore, the angles in Degrees are $72 °, 64 °, 96 °$ and $128 °$ .

Now convert these angles in radians using $1 ° = \frac{π^{c}}{180}$

So, $72 ° = \frac{π^{c}}{180} \times 72$

$\Rightarrow 72 ° = \frac{2 π^{c}}{5}, 64 ° = \frac{π^{c}}{180} \times 64 = \frac{16 π}{45}, 96 ° = \frac{π^{c}}{180} \times 96 = \frac{8 π^{c}}{5}$ and $128 ° = \frac{π^{c}}{180} \times 128 = \frac{32 π^{c}}{45}$

So, The angles in radians are $\frac{2 π}{5}, \frac{16 π}{45}, \frac{8 π}{15}$ and $\frac{32 π}{45}$ .

One angle of a quadrilateral has measure $\frac{2 π^{c}}{5}$ and the measures of other three angles are in the ratio $2 : 3 : 4 .$ Find their measures in degree and radian.

Important Questions on Angle and its Measurement

Learn and Prepare for any exam you want !

One angle of a quadrilateral has measure 2πc5 and the measures of other three angles are in the ratio 2: 3: 4 . Find their measures in degree and radian.

Important Questions on Angle and its Measurement

Learn and Prepare for any exam you want !

One angle of a quadrilateral has measure $\frac{2 π^{c}}{5}$ and the measures of other three angles are in the ratio $2 : 3 : 4 .$ Find their measures in degree and radian.