Question

The options are A. P= 65B. P= -25C. P= 115D. P= 25

Answer 1

The value of p is;

`p=25`

Step-by-step explanation:

From the given diagram;

Angle 4 and angle 6 are consecutive interior angles.

Applying the consecutive interior angle theorem. we have;

`m\angle4+m\angle6=180`

Given;

`\begin{gathered} m\angle4=(4p+15)^0 \\ m\angle6=(3p-10)^0 \end{gathered}`

Substituting the given expressions into the equation, we have;

`\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} \\ (7p)/(7)=(175)/(7) \\ p=25 \end{gathered}`

Therefore, the value of p is;

`p=25`