Question

answer attempt 1 out of 2
$p = $
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Explanation:

Step1: Identify angle - sum relationship

The two angles $(3p - 5)^{\circ}$ and $(5p+7)^{\circ}$ are complementary, so their sum is $90^{\circ}$. We set up the equation $(3p - 5)+(5p + 7)=90$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3p+5p-5 + 7=90$, 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 of the equation by 8: $\frac{8p}{8}=\frac{88}{8}$, so $p = 11$.

Answer:

$11$