Question

suppose that you know that $\angle t$ and $\angle s$ are supplementary, and that $m\angle t = 3 \cdot (m\angle s)$. complete the explanation for how you can find $m\angle t$. let $m\angle s = x$. first, you can write and solve an equation $(x + 3x = \square ^\circ)$ to find $x$. then (select) the value of $x$ by $\underline{\quad}$ to find $m\angle t$.

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles sum to \(180^\circ\). Since \(\angle T\) and \(\angle S\) are supplementary, \(m\angle T + m\angle S = 180^\circ\). Given \(m\angle S = x\) and \(m\angle T = 3x\), substitute into the equation: \(x + 3x = 180\).

Step2: Solve for \(x\) and Find \(m\angle T\)

First, combine like terms: \(4x = 180\). Then divide both sides by 4: \(x=\frac{180}{4} = 45\). To find \(m\angle T\), substitute \(x = 45\) into \(m\angle T = 3x\), so \(m\angle T = 3\times45 = 135\). The first blank is \(180\), the second operation is "multiplying by 3" (or "substituting into \(3x\)").

Answer:

First blank: \(180\); Second blank: multiplying by 3 (or substituting into \(3x\))