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m < U = 65°

Step-by-step explanation:

Given that m < PTU° = 115°, and that it is a supplement to < UTV, then we can establish that m < UTV = 65° because their angles must add up to 180°.

From this point forward, we'll name < UTV as < T of △VUT.

Now that we have the measure of < T, we can find out the value of the missing angle, < VUT, through the following equation:

180° = m < V° + m < T° + m < U°

180° =  m < 50° + m < 65° +  x

180° =  m < 115° +  x

Subtract m < 115 from both sides to isolate x:

180° -  m < 115° =  m < 115° - m < 115° +  x

65° = x

To verify that we have the correct answer, we'll add up all the measures of the three angles of the triangle to see if it sums up to 180°:

180° = m < V° + m < T° + m < U°

180° = m < 50° + m < 65° + m < 65°

180° = m < 50° + m < 65° + m < 65°

180°  = 180°  (True statement).

Therefore, the measure of the missing angle, < U = 65°

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