Question

vertical/adjacent/complementary angles (al question video examples solve for the value of $p$. answer attempt 1 out of 3 $p=$ submit answer copyright ©2025 deltamath.com all rights reserved. deltamath.com

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: Combine like terms

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

Step3: Isolate the term with \(p\)

Subtract \(2\) from both sides of the equation: \(8p+2-2=90 - 2\), so \(8p=88\).

Step4: Solve for \(p\)

Divide both sides by \(8\): \(p=\frac{88}{8}\).

Answer:

\(p = 11\)