Question

figure abcd is a parallelogram
what is the value of p?
(4p + 12)°
36°

Explanation:

Step1: Use the property of parallelogram

In a parallelogram \(ABCD\), \(AB\parallel CD\). So, \(\angle A=\angle C\) (alternate - interior angles are equal for parallel lines \(AB\) and \(CD\) with transversal \(AC\)).
We are given \(\angle A=(4p + 12)^{\circ}\) and \(\angle C = 36^{\circ}\).
So, \(4p+12 = 36\).

Step2: Solve the equation for \(p\)

Subtract \(12\) from both sides of the equation \(4p+12 = 36\).
\(4p+12-12=36 - 12\), which simplifies to \(4p=24\).
Divide both sides by \(4\): \(p=\frac{24}{4}\).

Answer:

\(6\)