Question

1 consider the following diagram.
lets focus on x first.
visually, the x parts of the diagram shows consecutive/sar angles.
this means that the angles are supplementary, which means that the two parts add up to 180 (part + part = 180)
to solve for x, a good equation to set up is therefore, and therefore x = 21
now lets do the y part.
suppose i choose to work with the 6x + 7 expression. (its a little bit easier that way.)

Explanation:

Step1: Set up the equation for \(x\)

Since the angles \((3x - 16)^{\circ}\) and \((6x + 7)^{\circ}\) are supplementary (add up to \(180^{\circ}\)), the equation is \((3x-16)+(6x + 7)=180\).
Simplify the left - hand side:

$$
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$$

Step2: Solve the equation for \(x\)

Add \(9\) to both sides of the equation \(9x-9 = 180\):
\(9x-9+9=180 + 9\), so \(9x=189\).
Divide both sides by \(9\): \(x=\frac{189}{9}=21\).

Answer:

The equation to set up for \(x\) is \((3x - 16)+(6x + 7)=180\) and \(x = 21\).