Question

unit 1 – lesson 3 exit ticket: given points r, t, and y shown below, do the following: (a) draw $overrightarrow{rt}$ and $overrightarrow{ry}$. (b) give the three-letter angle name for the angle you drew in (a). (two possibilities.) (c) using a protractor, find the measure of the angle from (b).

Explanation:

Part (a)

To draw \(\overrightarrow{RT}\) and \(\overrightarrow{RY}\), we first identify the points. Point \(R\) is the vertex (the starting point of the rays), \(T\) and \(Y\) are the other points. So, we draw a ray starting at \(R\) and passing through \(T\) (that's \(\overrightarrow{RT}\)) and another ray starting at \(R\) and passing through \(Y\) (that's \(\overrightarrow{RY}\)). Since the diagram of the points isn't fully shown here, but in general, we use a straightedge to draw these rays with \(R\) as the common endpoint.

Part (b)

The three - letter angle name is formed by the vertex in the middle and the other two points (one from each ray) on the ends. Since the vertex is \(R\), and the rays are \(\overrightarrow{RT}\) and \(\overrightarrow{RY}\), the two possible three - letter angle names are \(\angle TRY\) and \(\angle YRT\). In an angle name, the middle letter is always the vertex. So, we take the point on one ray (\(T\) or \(Y\)), then the vertex (\(R\)), then the point on the other ray (\(Y\) or \(T\)).

Part (c)

1. Step 1: Align the protractor

Place the center of the protractor on the vertex \(R\) of the angle. Align one of the rays (say \(\overrightarrow{RT}\)) with the \(0^{\circ}\) mark on the protractor (either the inner or outer scale, depending on the orientation of the ray).

1. Step 2: Read the measure

Then, look at where the other ray (\(\overrightarrow{RY}\)) intersects the protractor scale. The number of degrees at that intersection is the measure of the angle \(\angle TRY\) (or \(\angle YRT\)). Since we don't have the actual diagram with the drawn angle, if we assume a typical angle (for example, if the angle is, say, \(45^{\circ}\) or \(90^{\circ}\) or some other measure), but in a real - life situation, we would use the protractor to get the exact measure. For example, if when we align \(\overrightarrow{RT}\) with \(0^{\circ}\) and \(\overrightarrow{RY}\) aligns with \(60^{\circ}\) on the protractor, then the measure of the angle is \(60^{\circ}\).

Answer:

s:
(a) (Diagram: Rays from \(R\) through \(T\) and \(R\) through \(Y\))
(b) \(\boldsymbol{\angle TRY}\) and \(\boldsymbol{\angle YRT}\)
(c) (Depends on the actual angle, e.g., if measured as \(x^{\circ}\), the answer is \(x^{\circ}\), for example, if it's \(50^{\circ}\), then \(\boldsymbol{50^{\circ}}\))