Question

Examine the diagram, where quadrilateral MNOP is inscribed in ⨀C such that m∠P=(2x)∘ and m∠N=(2x−12)∘.

What is the measure of m∠P and m∠N?

m∠P=96∘, m∠N=84∘
m∠P=84∘, m∠N=72∘
m∠P=90∘, m∠N=90∘
m∠P=72∘, m∠N=108∘

Answer 1

Option (1)

Explanation:

Answer 2

Option (1)

Explanation:

Since quadrilateral MNOP is a cyclic quadrilateral, sum of opposite angles of the quadrilateral will be 180°.

m∠P + m∠N = 180°

(2x)° + (2x - 12)° = 180°

4x - 12 = 180

4x = 192

x = 48

Therefore, m∠P = (2x)° = 2×48 = 96°

m∠N = (2x - 12)° = (2×48) - 12 = 84°

Option (1) will be the answer.