Question

what is the value of p?
17b - 29°
p
10b
34°
p =

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(17b - 29=10b + 34\).

Step2: Solve for \(b\)

Subtract \(10b\) from both sides: \(17b-10b - 29=10b-10b + 34\), which simplifies to \(7b-29 = 34\).
Add \(29\) to both sides: \(7b-29 + 29=34 + 29\), so \(7b=63\).
Divide both sides by \(7\): \(b=\frac{63}{7}=9\).

Step3: Find the value of \(p\)

Since \(p = 10b\) (because \(p\) and \(10b\) are complementary to the exterior angle relationship in a right - triangle context, or we can use the fact that \(p\) is one of the non - exterior angles and we can also use the angle sum property of a triangle. But using the exterior angle related \(b\) value):
Substitute \(b = 9\) into \(p = 10b\), then \(p=10\times9 = 90\).

Answer:

\(90\)