Question
Download Solution PDFIn a cyclic quadrilateral MNOP, ∠M is opposite to ∠O, If 2∠O = 3∠M, then what is the value of ∠M?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A cyclic quadrilateral MNOP, where ∠M is opposite to ∠O.
2∠O = 3∠M
Concept Used:
In a cyclic quadrilateral, the sum of a pair of opposite angles is 180 degrees.
Calculation:
In a cyclic quadrilateral, the sum of a pair of opposite angles is 180 degrees.
Therefore, ∠M + ∠O = 180 degrees.
Since we know that 2∠O = 3∠M, we can express ∠O in terms of ∠M. Dividing the equation by 2, we get:
∠O = 1.5∠M
Substituting this into the formula ∠M + ∠O = 180 degrees, we get:
∠M + 1.5∠M = 180
2.5∠M = 180
∠M = 180/2.5
∠M = 72 degrees
So, the measure of ∠M is 72 degrees.
Last updated on Jul 10, 2025
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