Question

in a cyclic quadrilateral two adjacent angles are 40° and π/3 find the angles of quadrilateral in degree?​

Answer 1

Answer:

∠A=40° ,∠B=60°, ∠C=140° ,∠D=120°

Step-by-step explanation:

Let ABCD be the given cyclic quadrilateral.

Given:

∠A=40° and ∠B=60°

We know that sum of opposite angles a cyclic quadrilateral are supplementary

∠A+∠C=180°

∠B+∠D=180°

∠A+∠C=180°

⇒ 40°+∠C=180°

⇒ ∠C=180°-40°

⇒ ∠C=140°

∠B+∠D=180°

⇒ 60°+∠D=180°

⇒ ∠D=180°-60°

⇒ ∠D=120°

Hence

∠A=40° ,∠B=60°, ∠C=140° ,∠D=120°

Answer 2

In a cyclic quadrilateral two adjacent angles are 40° and π/3

two adjacent angles are 40° and π/3

π/3 = 180/3 = 60°

Sum of opposite angles in cyclic quadrilateral = 180°

Remaining two angles = 180° - 40° = 140°

& 180° - 60° = 120°  = 2π/3

40°*π/180° = 2π/9

140°*π/180° = 7π/9

All angles in deg & Radians

40° , 60° , 140° , 120°

2π/9 , π/3 , 7π/9 , 2π/3