Question

1. in the figure to the right, the two angles form a linear pair. find ( m angle d b c ).

Explanation:

Step1: Use linear pair property

Since the two angles \((5x + 10)^{\circ}\) and \((2x-5)^{\circ}\) form a linear pair, their sum is \(180^{\circ}\). So, \((5x + 10)+(2x - 5)=180\).

Step2: Simplify the equation

Combine like - terms: \(5x+2x+10 - 5=180\), which gives \(7x+5 = 180\).

Step3: Solve for \(x\)

Subtract \(5\) from both sides: \(7x=180 - 5=175\). Then divide both sides by \(7\): \(x=\frac{175}{7}=25\).

Step4: Find \(m\angle DBC\)

Substitute \(x = 25\) into \((2x-5)^{\circ}\). So, \(m\angle DBC=(2\times25 - 5)^{\circ}=(50 - 5)^{\circ}=45^{\circ}\).

Answer:

\(45^{\circ}\)