Question

12.
m
p
n
m∠p =

m∠n =

m∠m =

Explanation:

Step1: Identify isosceles - triangle properties

Since \(MP = NP\) and \(MN=NP\), \(\triangle MPN\) is equilateral. In an equilateral triangle, all angles are equal.

Step2: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). Let \(m\angle M=m\angle P = m\angle N=x\). Then \(x + x+x=180^{\circ}\).

Step3: Solve for the angle measure

\(3x = 180^{\circ}\), so \(x = 60^{\circ}\).

Answer:

\(m\angle M = 60^{\circ}\), \(m\angle N=60^{\circ}\), \(m\angle P = 60^{\circ}\)