Question

this quadrilateral is a kite. ∠b and ∠d are vertex angles. find ( mangle 4 ).

Explanation:

Step1: Use kite diagonal angle property

In a kite, the diagonal connecting vertex angles bisects those angles, and it is perpendicular to the other diagonal. So $\angle 4 = 90^\circ$.

Step2: Verify with triangle angle sum

In the triangle containing $\angle 4$, $72^\circ + \angle 4 + 18^\circ = 180^\circ$. Substitute $\angle 4 = 90^\circ$: $72 + 90 + 18 = 180$, which holds true.

Answer:

$m\angle 4 = 90^\circ$