# Spectrum Math Grade 4 Chapter 8 Lesson 1 Answer Key Points, Lines, Rays, and Angles

This handy Spectrum Math Grade 4 Answer Key Chapter 8 Lesson 8.1 Points, Lines, Rays, and Angles provides detailed answers for the workbook questions.

## Spectrum Math Grade 4 Chapter 8 Lesson 8.1 Points, Lines, Rays, and Angles Answers Key

The angle ABC (denoted ∠ABC) is made of ray BA ($$B \vec{A}$$) and ray BC ($$\overrightarrow{B C}$$). The point where the two rays intersect is called the vertex. The vertex of ∠ABC is point B.

An angle can be measured using a protractor. A protractor measures angles that range from 0° to 180°.

Identify or draw the rays and vertex of each angle. Name or label the angle.

Question 1.
a.

rays: _____________
vertex: ____________
angle: ____________
Rays: $$\overrightarrow{Q P}$$,$$\overrightarrow{Q R}$$
Vertex: Q
Angle: ∠PQR or ∠RQP
Explanation:
The angle ∠PQR is made of ray QP ($$\overrightarrow{Q P}$$) and ray QR ($$\overrightarrow{Q R}$$). The point where the two rays intersect is called the vertex. The vertex of ∠PQR is point Q.

b.

rays: _____________
vertex: ____________
angle: ____________
Rays: $$\overrightarrow{E D}$$,$$\overrightarrow{E F}$$
Vertex: E
Angle: ∠DEF or ∠FED
Explanation:
The angle ∠DEF is made of ray ED ($$\overrightarrow{E D}$$) and ray EF ($$\overrightarrow{E F}$$). The point where the two rays intersect is called the vertex. The vertex of ∠DEF is point E.

Question 2.
a. rays: $$\overrightarrow{L M}$$
$$\overrightarrow{M N}$$
vertex: M
angle: ∠LMN

Explanation:
The angle ∠LMN is made of ray LM ($$\overrightarrow{L M}$$) and ray MN ($$\overrightarrow{M N}$$). The point where the two rays intersect is called the vertex. The vertex of ∠LMN is point M. Drawn the rays, vertex of angle as we can observe in the above image.

b. rays: $$\overrightarrow{B C}$$
$$\overrightarrow{B A}$$
vertex: B
angle: ∠CBA

Explanation:
The angle ∠CBA is made of ray BC ($$\overrightarrow{B C}$$) and ray BA ($$\overrightarrow{B A}$$). The point where the two rays intersect is called the vertex. The vertex of ∠CBA is point B. Drawn the rays, vertex of angle as we can observe in the above image.
Identify an angle in each figure shown. Draw a figure for each angle given.

Question 3.
a.

angle: ______________
Angle: ∠123
Explanation:
In the above image we can observe an angle. The angle 123 is denoted as ∠123.

b.

angle: ______________
Angle: ∠RST or ∠TRS or ∠RTS
Explanation:
In the above image we can observe three angles. The first angle RST is denoted as ∠RST. The second angle TRS is denoted as ∠TRS. The third angle RTS is denoted as ∠RTS.

Question 4.
a. ∠XYZ