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

Answer:

6

Explanation:

Step1: Recall property of parallelogram

In parallelogram (ABCD), (\angle A+\angle D = 180^{\circ}) (adjacent - angles are supplementary).

Step2: Set up the equation

We know (\angle A=(4p + 12)^{\circ}) and (\angle D = 36^{\circ}), so ((4p + 12)+36=180).

Step3: Simplify the equation

(4p+48 = 180).

Step4: Isolate the variable term

Subtract 48 from both sides: (4p=180 - 48), so (4p = 132).

Step5: Solve for (p)

Divide both sides by 4: (p=\frac{132}{4}=33). (There is a mistake above, it should be (\angle A=\angle C) in a parallelogram. Since (\angle A=(4p + 12)^{\circ}) and (\angle C = 36^{\circ}), we set up the equation (4p+12 = 36).)

Step1 (corrected): Set up the correct equation

(4p+12 = 36).

Step2 (corrected): Isolate the variable - term

Subtract 12 from both sides: (4p=36 - 12), so (4p = 24).

Step3 (corrected): Solve for (p)

Divide both sides by 4: (p=\frac{24}{4}=6).