Question

1. find the values of x and y. (18y + 5)° (10x - 61)° (x + 10)°

Explanation:

Step1: Set up equation for x

Vertical - angles are equal. So, \(10x−61=x + 10\).
\[10x−x=10 + 61\]
\[9x=71\]
\[x=\frac{71}{9}\approx7.89\]

Step2: Set up equation for y

Assume the angles are supplementary (if they form a linear - pair). Let's assume the non - given angle related to \((18y + 5)^{\circ}\) is equal to \((x + 10)^{\circ}\) (vertically opposite to the known angle). If the two angles \((18y+5)\) and \((x + 10)\) are supplementary, then \((18y + 5)+(x + 10)=180\). Substitute \(x=\frac{71}{9}\) into the equation:
\[18y+5+\frac{71}{9}+10 = 180\]
\[18y+\frac{45 + 71+90}{9}=180\]
\[18y+\frac{206}{9}=180\]
\[18y=180-\frac{206}{9}\]
\[18y=\frac{1620 - 206}{9}=\frac{1414}{9}\]
\[y=\frac{1414}{9\times18}=\frac{707}{81}\approx8.73\]

Answer:

\(x=\frac{71}{9}\), \(y = \frac{707}{81}\)