Question

ABCD is a cyclic quadrilateral. find the value of x and y. Answer :- x = 40° and y = 25°. Please give step by step and correct solution. ​

Answer 1

Answer:

Answer :- x = 40° and y = 25°. Please give step by step and correct solution.

Answer 2

Answer:

x = 40°      y = 25°

Step-by-step explanation:

In cyclic quadilateral, we know that sum of opposite angles is equal to 180°.

∴ ∠B + ∠C = 180° - (i)

  ∠A + ∠D = 180°  - (ii)

In eq. (i),

∠B + ∠C = 180°

2x + 4° + 4y - 4° = 180°

2x + 4y = 180°

2 (x + 2y) = 180°

x + 2y = 180° ÷ 2

x + 2y = 90°

x = 90° - 2y

In eq.(ii),

∠A + ∠D = 180°

x + 10° + 5y + 5° = 180°

90° - 2y + 5y + 15° = 180°

3y + 105° = 180°

3y = 180° - 105°

3y = 75°

y = 75° ÷ 3

∴ y = 25°

⇒ x = 90° - 2y

⇒ x = 90° - 2 × 25°

⇒ x = 90° - 50°

⇒ x = 40°

∴ x = 40°      y = 25°