Question

solve for the value of p.

Explanation:

Step1: Recall angle - sum property

The sum of the angles around a point is 360°. Since one of the angles is a right - angle (90°), the sum of the other two non - right angles is 270°. So, (3p + 6)+(4p + 7)=270.

Step2: Combine like terms

Combine the p terms and the constant terms on the left - hand side. We get 3p+4p + 6 + 7=270, which simplifies to 7p+13 = 270.

Step3: Isolate the variable term

Subtract 13 from both sides of the equation. 7p+13−13=270−13, so 7p=257.

Step4: Solve for p

Divide both sides of the equation by 7. p = $\frac{257}{7}$ = 36.714 (approx) or p = 36$\frac{5}{7}$.

Answer:

p = 36$\frac{5}{7}$