Answer:
The value of p is;
[tex]p=25[/tex]
Explanation:
From the given diagram;
Angle 4 and angle 6 are consecutive interior angles.
Applying the consecutive interior angle theorem. we have;
[tex]m\angle4+m\angle6=180[/tex]
Given;
[tex]\begin{gathered} m\angle4=(4p+15)^0 \\ m\angle6=(3p-10)^0 \end{gathered}[/tex]
Substituting the given expressions into the equation, we have;
[tex]\begin{gathered} m\angle4+m\angle6=180 \\ 4p+15+3p-10=180 \\ 4p+3p+15-10=180 \\ 7p+5=180 \\ 7p=180-5 \\ 7p=175 \\ \text{divide both sides by 7} \\ \frac{7p}{7}=\frac{175}{7} \\ p=25 \end{gathered}[/tex]
Therefore, the value of p is;
[tex]p=25[/tex]
