Question

the diagram shows a triangle. what is the value of p? p =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(4p - 15)+(3p - 9)+113 = 180$.

Step2: Combine like - terms

$(4p+3p)+(-15 - 9 + 113)=180$, which simplifies to $7p+( - 24 + 113)=180$, and further to $7p + 89 = 180$.

Step3: Isolate the variable term

Subtract 89 from both sides: $7p=180 - 89$, so $7p = 91$.

Step4: Solve for p

Divide both sides by 7: $p=\frac{91}{7}=13$.

Answer:

$13$