Question

4.find both the value of x and the value of the missing angle measure (not just the value of x).

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(45^{\circ}+65^{\circ}+5x = 180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add \(45^{\circ}\) and \(65^{\circ}\): \(45 + 65+5x=180\), which simplifies to \(110+5x = 180\).

Step3: Solve for \(x\)

Subtract \(110\) from both sides: \(5x=180 - 110\), so \(5x = 70\). Then divide both sides by \(5\): \(x=\frac{70}{5}=14\).

Step4: Find the measure of the missing angle

The missing angle is \(5x\). Substitute \(x = 14\) into \(5x\), so \(5x=5\times14 = 70^{\circ}\).

Answer:

\(x = 14\) and the missing angle measure is \(70^{\circ}\)