Question

1. if \\( \angle abd = 2x + 7 \\) and \\( \angle dbc = 8x + 13 \\), what is the value of x?

Explanation:

Step1: Use the linear - pair relationship

Since \(\angle ABD\) and \(\angle DBC\) form a linear pair, \(\angle ABD+\angle DBC = 180^{\circ}\).
Given \(\angle ABD=2x + 7\) and \(\angle DBC=8x + 13\), we substitute these into the equation: \((2x + 7)+(8x + 13)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+8x+7 + 13=180\), which simplifies to \(10x+20 = 180\).

Step3: Solve for \(x\)

Subtract 20 from both sides: \(10x+20-20=180 - 20\), so \(10x=160\).
Divide both sides by 10: \(x=\frac{160}{10}\).

Answer:

\(x = 16\)