Question

turn and talk: reflex angles are defined in terms of a given angle; they are considered the \other half\ of an acute, right, or obtuse angle. together, an angle and its reflex angle form a complete rotation, or full angle of 360°. pick two angles from task 2 and find the measure of their reflex angle. if the measure of an angle is x°, what is the measure of its reflex angle? bisect an angle: to bisect a figure is to divide it into two congruent parts. the angle bisector of an angle is a ray that divides the angle into two congruent angles. you can write a congruence statement about angles using the same symbol you used for segments: ∠a≅∠b. task 3: draw an estimate of the angle bisector and give the measurements. a. the angle to the right measures 46°. draw an estimated bisector of the angle and determine the measure of the two newly - formed adjacent angles.

Explanation:

Step1: Find reflex - angle formula

Since an angle and its reflex angle form a full - rotation of 360°, if the measure of an angle is \(x^{\circ}\), the measure of its reflex angle \(y\) is given by \(y = 360 - x\).

Step2: Bisect the 46° angle

The angle bisector divides an angle into two congruent parts. If the original angle \(\theta=46^{\circ}\), then each of the two newly - formed adjacent angles \(\alpha\) after bisection is \(\alpha=\frac{46}{2}\).

Answer:

1. The measure of the reflex angle of an angle \(x^{\circ}\) is \((360 - x)^{\circ}\).
2. When bisecting a 46° angle, each of the two newly - formed adjacent angles has a measure of 23°.