Question

1. find the measure of ∠2.

options: 60°, 54°, 72°, 36°

Explanation:

Step1: Identify the polygon type

The shape is a regular pentagon (5 sides).

Step2: Calculate central angle

Central angle = $\frac{360^\circ}{5} = 72^\circ$ (angle 1).

Step3: Analyze triangle with right angle

The triangle with angle 3 and right angle is isosceles (radii equal). So angle 3 = $\frac{180^\circ - 90^\circ}{2} = 45^\circ$? No, wait—correction: The dashed lines from center to vertices divide the pentagon into 5 congruent isosceles triangles. Each has vertex angle 72°, base angles = $\frac{180^\circ - 72^\circ}{2} = 54^\circ$. Angle 2 is one of these base angles.

Step4: Confirm angle 2

Angle 2 equals the base angle of the isosceles triangle, so 54°.

Answer:

54°