Question

solve for the value of p.

Explanation:

Step1: Set up equation

Assume the two - angle expressions sum to 90° (since they seem to form a right - angle). So, $(5p + 7)+(3p-5)=90$.

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 variable term

Subtract 2 from both sides of the equation: $8p+2-2=90 - 2$, resulting in $8p=88$.

Step4: Solve for $p$

Divide both sides by 8: $\frac{8p}{8}=\frac{88}{8}$, so $p = 11$.

Answer:

$11$