Question

question le: find mllpn if ∠3 is a right angle and ∠mpn ≅ ∠rpn

Explanation:

Step1: Determine the measure of \(\angle LPN\)

Since \(\angle3\) is a right - angle, \(\angle3 = 90^{\circ}\). And because \(\angle MPN\cong\angle RPN\), the sum of \(\angle MPN\) and \(\angle RPN\) is equal to \(\angle LPN\).

Step2: Calculate the measure of \(\angle LPN\)

Let \(\angle MPN=\angle RPN = x\). Then \(\angle LPN=\angle MPN+\angle RPN\). Since \(\angle3 = 90^{\circ}\) and \(\angle MPN\cong\angle RPN\), we know that \(\angle LPN = 45^{\circ}\) (because if two angles are congruent and their sum is \(90^{\circ}\), then each angle \(x=\frac{90^{\circ}}{2}\)).

Answer:

\(45^{\circ}\)