Question

what are the values of v and p? v = \\( \square ^ { \circ } \\) p = \\( \square ^ { \circ } \\)

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(14v=(v + 44)+(4v + 46)\)

Step2: Simplify the equation

Expand the right - hand side: \(14v=v + 44+4v + 46\)
Combine like terms: \(14v=5v+90\)
Subtract \(5v\) from both sides: \(14v−5v=5v + 90−5v\)
\(9v=90\)
Divide both sides by \(9\): \(v=\frac{90}{9}=10\)

Step3: Find the value of \(2p\)

First, find the measure of the non - labeled interior angle. The sum of angles in a triangle is \(180^{\circ}\). Let the non - labeled interior angle be \(x\). Then \(x = 180-(v + 44)-(4v + 46)\)
Substitute \(v = 10\): \(x=180-(10 + 44)-(4\times10+46)=180 - 54-86 = 40\)
Since \(14v=2p+x\) and \(v = 10\), \(14\times10=2p + 40\)
\(140=2p+40\)
Subtract \(40\) from both sides: \(140−40=2p+40−40\)
\(100=2p\)
Divide both sides by \(2\): \(p = 50\)

Answer:

\(v = 10\), \(p = 50\)