Question

the greatest angle of a cyclic quadrilateral is double the least and the difference of the two angles is 30 degree find the angles in degrees and radians

Answer 1

check question again for my help..... thanks

Answer 2

Answer:

Angles are 30°, 60°, 105° and 75°(in degree)

Angles are π/6, π/3, 5π/12, 7π/12(in radian).

Step-by-step explanation:

Let ABCD be a quadrilateral.

We know that the sum of the opposite angles of a cyclic quadrilateral is always equal to 180°.

So, if  ∠A is greater then ∠C must be lesser.

∠A + ∠C = 180°

Given: ∠A = 2∠C

2∠C  + ∠C = 180°

3∠C = 180°

∠C = 60°

Therefore ∠C = 60°

than ∠A will be the double of ∠C  

∠ A = 120°

Also ∠B+∠D = 180°

Let ∠B – ∠D = 30°

Hence ∠B = 105° and ∠D = 75°

∠ A = 120°, ∠B = 105°, ∠C = 60°, ∠D = 75°.

Angles are 30°, 60°, 105° and 75°(in degree)

$\text {degree} = \dfrac {\pi}{180^o} \times \text{Radian}$

$30^o = \dfrac {\pi}{180^o} \times 30^o \text{Radian} = \dfrac {\pi}6\text{Radian}\\\\60^o = \dfrac {\pi}{180^o} \times 60^o \text{Radian} = \dfrac {\pi}3\text{Radian}\\\\75^o = \dfrac {\pi}{180^o} \times 75^o \text{Radian} = \dfrac {5\pi}{12}\text{Radian}\\105^o = \dfrac {\pi}{180^o} \times 105^o \text{Radian} = \dfrac {7\pi}{12}\text{Radian}$

Angles are π/6, π/3, 5π/12, 7π/12(in radian).