Question

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

Explanation:

Step1: Use vertical - angle property

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

Step2: Solve for \(x\)

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

Step3: Use the fact that the sum of adjacent angles is 180° (assuming linear - pair)

Let's assume the angles \((18y + 5)\) and \((x + 10)\) are supplementary (a linear - pair). So, \((18y + 5)+(x + 10)=180\). Substitute \(x=\frac{71}{9}\) into the equation: \(18y+5+\frac{71}{9}+10 = 180\). First, combine the constant terms: \(18y+15+\frac{71}{9}=180\). Then, \(18y=180 - 15-\frac{71}{9}\). \(180-15 = 165\), so \(18y=165-\frac{71}{9}\). \(165=\frac{1485}{9}\), then \(18y=\frac{1485 - 71}{9}=\frac{1414}{9}\). \(y=\frac{1414}{9\times18}=\frac{707}{81}\approx8.73\).

Answer:

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