Answer:
∠QPO = 82°
Step-by-step explanation:
In a rhombus, opposite angles are congruent. Therefore, in rhombus MNOP, angle PMN is congruent to angle PON. Given that ∠PMN = 76°, it follows that ∠PON = 76°.
In a kite, the angles between the pairs of sides that are of unequal length are congruent. Given that ∠PQN = 120° and ∠PON = 76°, the angles QNO and QPO must be congruent.
The interior angles of a kite sum to 360°. Therefore, to find the size of angle QPO, subtract the measures of angles PQN and PON from 360°, then divide the result by 2:
[tex]\sf \angle QPO=\dfrac{360^{\circ}-\angle PQN - \angle PON}{2} \\\\\\ \angle QPO=\dfrac{360^{\circ}-120^{\circ} -76^{\circ}}{2} \\\\\\ \angle QPO=\dfrac{164^{\circ}}{2} \\\\\\\angle QPO=82^{\circ}[/tex]
Therefore, the size of angle QPO is 82°.
