1. The balance a. Classify the relationship between $$ \angle x $$ and $$ \angle y $$. b. If $$ m \angle y=117^{\circ} $$, find the value of $$ x $$.

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**Step 1. Classifying the Relationship**

Since the angles $$ x $$ and $$ y $$ are described in the context of a balance (often implying a straight line), we conclude that they form a linear pair. Linear pairs are supplementary, meaning that

$$
m\angle x + m\angle y = 180^\circ.
$$

**Step 2. Solving for $$ x $$**

We are given $$ m\angle y = 117^\circ $$. Using the supplementary relationship:

$$
m\angle x = 180^\circ - m\angle y = 180^\circ - 117^\circ.
$$

Calculating this, we get

$$
m\angle x = 63^\circ.
$$

Thus, the value of $$ x $$ is $$ 63^\circ $$.
**a.** Angles $$ x $$ and $$ y $$ are supplementary, forming a linear pair. **b.** If $$ m\angle y = 117^\circ $$, then $$ x = 63^\circ $$.

The balance
a. Classify the relationship between and .
b. If , find the value of .

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The balance a. Classify the relationship between and . b. If , find the value of .