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: Apply 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, \(18p - 8=(p + 47)+33\).

Step2: Simplify the right - hand side

Simplify \((p + 47)+33\) to get \(p+80\). The equation becomes \(18p - 8=p + 80\).

Step3: Solve for \(p\)

Subtract \(p\) from both sides: \(18p-p-8=p - p+80\), which simplifies to \(17p-8 = 80\).
Add \(8\) to both sides: \(17p-8 + 8=80 + 8\), so \(17p=88\).
Divide both sides by \(17\): \(p=\frac{88}{17}\approx5.2\).

Answer:

\(p = 5.2\)