Question

1. calculate the value of x in the following diagram.

x + 5, 4x + 10

Explanation:

Step1: Identify the angle relationship

The two angles form a linear pair, so their sum is \(180^\circ\). Thus, \((x + 5)+(4x + 10)=180\).

Step2: Combine like terms

Simplify the left - hand side: \(x+5 + 4x+10=5x + 15\). So the equation becomes \(5x+15 = 180\).

Step3: Solve for x

Subtract 15 from both sides: \(5x=180 - 15=165\). Then divide both sides by 5: \(x=\frac{165}{5}=33\).

Answer:

\(x = 33\)