Question

wednesday

1. which angle is bigger?

∠a or ∠b

1. how many degrees is a

circle?

1. is ⌢ab

major
or
minor?

Explanation:

1. Which angle is bigger? $\angle A$ or $\angle B$

Step1: Recall the definition of central angle and inscribed angle

A central angle ($\angle A$) is an angle whose vertex is at the center of a circle. An inscribed angle ($\angle B$) is an angle whose vertex is on the circumference of a circle. For a given arc, the measure of a central angle is twice the measure of an inscribed angle that subtends the same arc.

Step2: Compare the measures

Let the arc subtended by both angles be \(x\). The measure of \(\angle A\) (central angle) is \(x\) degrees. The measure of \(\angle B\) (inscribed angle) is \(\frac{x}{2}\) degrees. Since \(x>\frac{x}{2}\) (assuming \(x > 0\)), \(\angle A\) is bigger.

2. How many degrees is a circle?

A full - circle is a complete rotation. By the definition of an angle measure in a circle, a full - circle has \(360^{\circ}\).

3. Is $\overset{\frown}{AB}$ major or minor?

Step1: Recall the definitions

A minor arc is an arc that is less than a semicircle (less than \(180^{\circ}\)). A major arc is an arc that is more than a semicircle (more than \(180^{\circ}\)).

Step2: Determine from the figure

Since the arc \(\overset{\frown}{AB}\) is less than a semicircle (the non - arc part is larger), \(\overset{\frown}{AB}\) is a minor arc.

Answer:

1. \(\angle A\) is bigger.
2. \(360^{\circ}\)
3. Minor arc.