Question

is the measure of angle x?

Explanation:

Step1: Identify right - triangle sides

Assume the grid squares have side - length 1. We can find the opposite and adjacent sides of angle \(x\) from the grid. Let the opposite side \(a\) and adjacent side \(b\). By counting the grid squares, if we consider the right - triangle formed by angle \(x\), assume the opposite side \(a = 4\) and the adjacent side \(b = 4\).

Step2: Use tangent function

The tangent of an angle in a right - triangle is defined as \(\tan(x)=\frac{a}{b}\). Substituting \(a = 4\) and \(b = 4\) into the formula, we get \(\tan(x)=\frac{4}{4}=1\).

Step3: Find the angle

We know that if \(\tan(x)=1\), and \(x\) is an acute angle, then \(x = 45^{\circ}\) since \(\tan(45^{\circ}) = 1\).

Answer:

\(45^{\circ}\)