Question

1. this figure is a detail of one vertex of the tiling at the beginning of this lesson. find the missing angle measure x.

Explanation:

Step1: Recall the sum of angles around a point

The sum of angles around a point is \(360^{\circ}\).

Step2: Identify known angles

We have two right - angles (\(90^{\circ}\) each) and a \(60^{\circ}\) angle. Let the unknown angle be \(x\).

Step3: Set up the equation

Using the sum of angles around a point formula: \(90^{\circ}+90^{\circ}+60^{\circ}+x = 360^{\circ}\).

Step4: Simplify the left - hand side

\(240^{\circ}+x=360^{\circ}\).

Step5: Solve for \(x\)

Subtract \(240^{\circ}\) from both sides: \(x = 360^{\circ}-240^{\circ}\).

Answer:

\(x = 120^{\circ}\)