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° + 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°
