Question

1. what is m∠p? ____________

Explanation:

Step1: Recall sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is $(4 - 2)\times180^{\circ}=360^{\circ}$.

Step2: Set up an equation for the angles of the second - quadrilateral

Let $m\angle P=x$. We know that $m\angle Q = 107^{\circ}$, $m\angle R$ is unknown, $m\angle S=115^{\circ}$, and for a quadrilateral $x + 107^{\circ}+m\angle R+115^{\circ}=360^{\circ}$. Since the two quadrilaterals are congruent (sides are equal: $AB = QR = 22$ in and $CD=PS = 28$ in), we can also use the angle - sum property directly for the second quadrilateral.
We have $x+107^{\circ}+115^{\circ}+\text{(the fourth angle)}=360^{\circ}$.
We know that in a quadrilateral, if we call the fourth angle $y$, then $x + 107^{\circ}+115^{\circ}+y=360^{\circ}$.
We can also note that the corresponding angles of congruent quadrilaterals are equal. But using the angle - sum formula:
$x=360^{\circ}-(107^{\circ}+115^{\circ})$
$x = 360^{\circ}-222^{\circ}$
$x = 138^{\circ}$

Answer:

$138^{\circ}$