Question

problem 9: from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: △suv, m∠s = 15, and m∠u = 50 prove: m∠svu = 115

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So for $\triangle SUV$, we have $m\angle S+m\angle U + m\angle SVU=180^{\circ}$.

Step2: Substitute given values

We know $m\angle S = 15^{\circ}$ and $m\angle U = 50^{\circ}$. Substituting into the equation: $15 + 50+m\angle SVU=180$.

Step3: Solve for $m\angle SVU$

First, simplify the left - hand side: $65+m\angle SVU=180$. Then subtract 65 from both sides: $m\angle SVU=180 - 65=115^{\circ}$. So the theorem that justifies the proof is the sum - of - angles in a triangle theorem.

Answer:

The sum - of - angles in a triangle theorem.