Question

1. what is the measure of angle bed? (think about what shapes you see in the figure) 28. what is the measure of angle bdc? use the following picture of a regular polygon for questions 34 and 35.

Explanation:

Step1: Find the measure of each interior angle of a regular hexagon

The formula for the measure of each interior angle of a regular polygon is \(\frac{(n - 2)\times180^{\circ}}{n}\), where \(n = 6\) (for a hexagon).
\(\frac{(6 - 2)\times180^{\circ}}{6}=\frac{4\times180^{\circ}}{6}=120^{\circ}\). So, \(\angle AED=\angle EDC = 120^{\circ}\).

Step2: Analyze triangle \(BED\)

Since \(AB = BC=CD = DE = EF=FA\) (regular hexagon), and \(BE = BD\) (by symmetry in the regular hexagon). In triangle \(BED\), \(\angle EDB=\angle EBD\). \(\angle BED = 120^{\circ}\) (interior angle of the hexagon).

Step3: Analyze triangle \(BDC\)

In right - angled triangle \(BDC\) (we know from the properties of the regular hexagon and the figure, \(\angle EDC = 120^{\circ}\), \(\angle EDB = 30^{\circ}\) (from triangle \(BED\) where \(\angle BED=120^{\circ}\), \(\angle EDB=\frac{180^{\circ}-\angle BED}{2}=\frac{180 - 120}{2}=30^{\circ}\)), \(\angle BDC=\angle EDC-\angle EDB\).

Answer:

1. \(120^{\circ}\)
2. \(90^{\circ}\)