Question

Quantity A: Double the measure of a single interior angle of an equilateral triangle.
Quantity B: The measure of a single interior angle of a (regular) hexagon.
Which statement is true?

• A. The relationship cannot be determined with the information given.
• B. Quantity B is bigger.
• C. The quantities are equal.
• D. Quantity A is bigger.
• E.

Hint:

Memorize common regular polygons: triangle \(60^\circ\), square \(90^\circ\), pentagon \(108^\circ\), hexagon \(120^\circ\).

Answer 1

The Correct Option is C

Step 1: Interior angle of an equilateral triangle.
Each interior angle \(= 60^\circ\). Double \(\Rightarrow 120^\circ\).
Step 2: Interior angle of a regular hexagon.
For a regular \(n\)-gon, each interior angle is \(\dfrac{(n-2)180^\circ}{n}\).
For \(n=6\): \(\dfrac{4 \cdot 180^\circ}{6} = 120^\circ\).
Step 3: Compare.
Both are \(120^\circ\) \(\Rightarrow\) \(\boxed{\text{Quantities are equal}}\).