Question

1. rhombus

m∠pmn = 110

Explanation:

Step1: Recall rhombus angle property

In a rhombus, the diagonal bisects the vertex angle. So $\angle PMO = \angle NMO = 5x^\circ$, and $\angle PMN = \angle PMO + \angle NMO$.

Step2: Set up the equation

Substitute the known value: $110^\circ = 5x^\circ + 5x^\circ$
Simplify the right-hand side: $110 = 10x$

Step3: Solve for $x$

Divide both sides by 10: $x = \frac{110}{10}$

Answer:

$x = 11$