Question

find ( mangle krl ).
( mangle krl=)

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. The angle opposite to \(56^{\circ}\) (let's call it \(\angle QRH\)) is equal to \(56^{\circ}\) because of the vertical - angle theorem.

Step2: Use the right - angle relationship

\(\angle KRM = 90^{\circ}\). We know that \(\angle KRL+\angle LRM=\angle KRM\). Also, \(\angle LRM\) and the \(56^{\circ}\) angle (\(\angle QRH\)) are vertical angles, so \(\angle LRM = 56^{\circ}\).

Step3: Calculate \(m\angle KRL\)

Using the equation \(\angle KRL=90^{\circ}-\angle LRM\). Substitute \(\angle LRM = 56^{\circ}\) into the equation: \(\angle KRL=90 - 56\).

Answer:

\(34\)