Question

given the diagram shown here, if (mangle8 = 17p + 11) and (mangle4 = 127 - 3p), what is the value of (p)? (p = 2) (p = 3) (p = 5.8)

Explanation:

Answer:

Since \( \angle8 \) and \( \angle4 \) are corresponding angles (assuming the lines are parallel as is common in such set - ups), they are equal. So we set up the equation \(17p + 11=127 - 3p\).

First, add \(3p\) to both sides: \(17p+3p + 11=127-3p + 3p\), which simplifies to \(20p+11 = 127\).

Then subtract \(11\) from both sides: \(20p+11 - 11=127 - 11\), giving \(20p=116\).

Finally, divide both sides by \(20\): \(p=\frac{116}{20}=5.8\)

So the answer is \(p = 5.8\)