Question

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

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(10x−61=x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(10x−x−61=x−x + 10\), which simplifies to \(9x−61 = 10\). Then add 61 to both sides: \(9x−61+61=10 + 61\), getting \(9x=71\), and \(x=\frac{71}{9}\approx7.89\).

Step3: Use the fact that adjacent angles are supplementary

Let's assume the adjacent - angle relationship. If we consider the linear - pair or other angle - sum property (assuming the angles are part of a linear pair or a known angle - sum situation). But if we assume the two non - vertical angles are supplementary (a common case in angle problems with intersecting lines), we have no information about the third angle related to \((18y + 5)\) to form an equation. However, if we assume the two non - vertical angles are vertical to each other, then \(18y+5=x + 10\). Substitute \(x=\frac{71}{9}\) into the equation: \(18y+5=\frac{71}{9}+10\). First, simplify the right - hand side: \(\frac{71}{9}+10=\frac{71 + 90}{9}=\frac{161}{9}\). Then, \(18y=\frac{161}{9}-5=\frac{161-45}{9}=\frac{116}{9}\), and \(y=\frac{116}{9\times18}=\frac{58}{81}\approx0.72\).

Answer:

\(x=\frac{71}{9},y = \frac{58}{81}\)