Answer: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° + x180° = m < 115° + xSubtract m < 115 from both sides to isolate x:180° - m < 115° = m < 115° - m < 115° + x65° = xTo 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°