Question

in a cyclic quadrilateral PQRS, P = (2x - 1), Q = (y + 5), R = (2y -15) and S = (4x - 7) then the value of Q is:​

Answer 1

Answer:

75 degree is your correct answer

Step-by-step explanation:

Answer 2

Given :- in a cyclic quadrilateral PQRS, ∠P = (2x - 1),

∠Q = (y + 5), ∠R = (2y - 15), ∠S = (4x - 7) .

To Find :- ∠Q = ?

Concept used :-

• In a cyclic quadrilateral sum of opposite angles is equal to 180° .

Solution :-

from above told concept we get,

• ∠P + ∠R = 180°
• ∠Q + ∠S = 180°

So, putting given values we get,

→ (2x - 1) + (2y - 15) = 180°

→ 2x + 2y - 16 = 180°

→ 2x + 2y = 180° + 16°

→ 2(x + y) = 196°

→ x + y = 98° ------------- Equation (1)

similarly,

→ (y + 5) + (4x - 7) = 180°

→ y + 4x - 2 = 180°

→ y + 4x = 182° ------------- Equation (2)

subtracting Equation (1) from Equation (2),

→ (y + 4x) - (x + y) = 182° - 98°

→ y - y + 4x - x = 84°

→ 3x = 84°

→ x = 28°

putting value of x in Equation (1),

→ y + 28° = 98°

→ y = 98° - 28°

→ y = 70°

therefore,

→ ∠Q = y + 5

→ ∠Q = 70° + 5°

→ ∠Q = 75° (Ans.)

Hence, the value of ∠Q is equal to 75° .

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