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CMerrill · Answer 1 · 2023-08-21T19:19:02+0000

Answer:

Substitution

Step-by-step explanation:

We are to complete the proof that:

m∠U + m∠Y + m∠UVY = 180° (without using the Triangle Angle Sum Theorem)

This is proven below given the following statements:

$\begin{gathered} m\angle UVY+m\angle WVY=180^(\circ) \\ But:m\angle WVY=m\angle U+m\angle Y \\ \text{Substituting this into the initial formula, we have:} \\ \operatorname{\Rightarrow}m\operatorname{\angle}UVY+m\operatorname{\angle}U+m\operatorname{\angle}Y=180^{\operatorname{\circ}} \\ m\operatorname{\angle}U+m\operatorname{\angle}Y+m\operatorname{\angle}UVY=180^{\operatorname{\circ}} \\ \\ m\operatorname{\angle}U+m\operatorname{\angle}Y+m\operatorname{\angle}UVY=180^{\operatorname{\circ}}(Substitution) \end{gathered}$

Therefore, the answer is Substitution

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