Question

Given the following diagram, find the missing measure.

Given:



m 2 = 30°, m P =

30
60
90
120

Answer 1

m 2 = 30°, m P = 60

The correct choice is 60

Answer 2

Measure of ∠P = 60°

Explanation:

Consider triangle PMO.

Since PM is perpendicular to MO , hence m∠PMO = 90°

Also given that m∠MOP = m∠2 = 30°

And since sum of three angles of a triangle is 180°

⇒ m∠PMO + m∠MOP + m∠MPO = 180°

⇒m∠MPO = 180° - (m∠PMO + m∠MOP) = 180° - ( 90 + 30 ) = 60°

Hence m∠MPO that is m∠P is 60°