Question

what is the value of p?
write your answer as an integer or as a decimal rounded to the nearest tenth.
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, \(15p - 38=(3p + 23)+6p\).

Step2: Simplify the right - hand side

Simplify \((3p + 23)+6p\) to get \(9p + 23\). So the equation becomes \(15p-38 = 9p+23\).

Step3: Solve for \(p\)

Subtract \(9p\) from both sides: \(15p-9p-38=9p - 9p+23\), which simplifies to \(6p-38 = 23\).
Add \(38\) to both sides: \(6p-38 + 38=23+38\), so \(6p=61\).
Divide both sides by \(6\): \(p=\frac{61}{6}\approx10.2\).

Answer:

\(10.2\)