Question

what is the value of p?
31°
4p-20°
p+50°
p = □°
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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, \(31^{\circ}+(4p - 20)^{\circ}=(p + 50)^{\circ}\)

Step2: Simplify the equation

$$
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$$

Step3: Solve for \(p\)

Subtract \(p\) from both sides: \(4p - p+11=p - p + 50\), which gives \(3p+11 = 50\)
Subtract \(11\) from both sides: \(3p+11-11=50 - 11\), so \(3p=39\)
Divide both sides by \(3\): \(p=\frac{39}{3}=13\)

Answer:

\(13\)