Question

solve for the value of p.
answer attempt 1 out of 2
p =

Explanation:

Step1: Set up the equation

Since the two angles \((5p + 7)^{\circ}\) and \((3p - 5)^{\circ}\) are complementary (they form a right - angle, so their sum is \(90^{\circ}\)), we have the equation \(5p+7+3p - 5=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((5p+3p)+(7 - 5)=90\), which simplifies to \(8p+2 = 90\).

Step3: Solve for \(p\)

Subtract 2 from both sides: \(8p=90 - 2\), so \(8p=88\). Then divide both sides by 8: \(p=\frac{88}{8}=11\).

Answer:

\( p = 11 \)