Question

Q.11 In a cyclic quadrilateral two adjacent
angles are 40° and . Find the angles
of the quadrilateral in degree.​

Answer 1

Answer:

∠A=40°, ∠B=40°, ∠C=140° and ∠D=140°

Step-by-step explanation:

Concept used:

Opposite angles of a cyclic quarilateral are supplementary

Let ABCD be cyclic quadrilateral with

∠A=40° and ∠B=40°

since the opposite angles are supplementary,

∠A+∠C=180° and ∠B+∠D=180°

40°+∠C=180° and 40°+∠D=180°

∠C=180°-40° and ∠D=180°-40°

⇒ ∠C=140° and ∠D=140°

Answer 2

Answer:

40° , 60° , 140° , 120°

2π/9 , π/3 , 7π/9 , 2π/3

Step-by-step explanation:

Complete data is :

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