Question
Download Solution PDFPQRS is a cyclic quadrilateral In PQRS ∠P is opposite to ∠R. If ∠P and ∠R are 3x + 5 and 4x respectively, then what is the value of x?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
PQRS is a cyclic quadrilateral.
∠P is opposite to ∠R.
∠P and ∠R are 3x + 5 and 4x respectively.
Concept Used:
In a cyclic quadrilateral, the sum of a pair of opposite angles is 180 degrees.
Calculation:
Since angle P and angle R are opposite to each other, we have:
∠P + ∠R = 180°
Given that ∠P = 3x + 5 and ∠R = 4x, we can substitute these values into the equation:
(3x + 5) + 4x = 180
Solving for x:
⇒ 7x + 5 = 180
⇒ 7x = 175
⇒ x = 175 / 7
⇒ x = 25
So, the value of x is 25.
Last updated on May 28, 2025
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