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: ____________

Answer:

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: ____________

Answer:

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

Answer:

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

Answer:

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: ______________

Answer:

Angle: ∠123

Explanation:

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

b.

angle: ______________

Answer:

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

Answer:

Explanation:

The angle ∠XYZ is drawn as we can observe in the above image.

b. ∠678

Answer:

Explanation:

The angle ∠678 is drawn as we can observe in the above image.