what is the value of p? p =

Answer:

11

Explanation:

Step1: Recall angle - sum property of a quadrilateral

The sum of interior angles of a quadrilateral is $360^{\circ}$. In the given quadrilateral $TSRQ$, we have two right - angles ($90^{\circ}$ each), and two angles of $44^{\circ}$ each.

Step2: Set up the equation

$90 + 90+44 + 44+(3p)+(p + 4)=360$.

Step3: Simplify the left - hand side of the equation

First, add the constant terms: $90+90 + 44+44+4=272$. Then, combine the $p$ terms: $3p + p=4p$. So the equation becomes $272+4p=360$.

Step4: Solve for $p$

Subtract 272 from both sides: $4p=360 - 272$. So $4p = 88$. Then divide both sides by 4: $p=\frac{88}{4}=11$.