Chapter 2.7, Problem 29SPR

To determine

To find:The degree measure of the numbered angles.

Answer to Problem 29SPR

The degree of pattern blocks are given below.

Explanation of Solution

Given information:

The pattern blocks are arranged in a circular pattern. Measurement around a circle is ${360}^{\text{o}}$ .

  

Figure $\left(1\right)$

Calculation:

Consider the pattern blocks,

  $1.$

In the first block, draw an inner circle. And the circle is divided into ${360}^{\text{o}}$ .

Now, split the circle into $6$ parts.

Calculate the angle $\angle 1$

  $\begin{array}{l}m\angle 1=\frac{{360}^{\text{o}}}{6}\\ m\angle 1={60}^{\text{o}}\end{array}$

Therefore, the angle $\angle 1$ is ${60}^{\text{o}}$ .

  $2.$

In the second block, draw an inner circle. And the circle is divided into ${360}^{\text{o}}$ .

Now, split the circle into $12$ parts.

Calculate the angle $\angle 2$ ,

  $\begin{array}{l}m\angle 2=\frac{{360}^{\text{o}}}{12}\\ m\angle 2={30}^{\text{o}}\end{array}$

Therefore, the angle $\angle 2$ is ${30}^{\text{o}}$ .

  $3.$

In the third block, draw an inner circle. And the circle is divided into ${360}^{\text{o}}$ .

Now, split the circle into $4$ parts.

Calculate the angle $\angle 3$ ,

  $\begin{array}{l}m\angle 3=\frac{{360}^{\text{o}}}{4}\\ m\angle 3={90}^{\text{o}}\end{array}$

Therefore, the angle $\angle 3$ is ${90}^{\text{o}}$ .

  $4.$

In the first block, draw an inner circle. And the circle is divided into ${360}^{\text{o}}$ .

Now, split the circle into $6$ parts.

Calculate the angle $\angle 4$ ,

  $\begin{array}{l}m\angle 4=\frac{{360}^{\text{o}}}{6}\\ m\angle 4={60}^{\text{o}}\end{array}$

Therefore, the angle $\angle 4$ is ${60}^{\text{o}}$ .

  $5.$

In the first block, draw an inner circle. And the circle is divided into ${360}^{\text{o}}$ .

Now, split the circle into $3$ parts.

Calculate the angle $\angle 5$ ,

  $\begin{array}{l}m\angle 5=\frac{{360}^{\text{o}}}{3}\\ m\angle 5={120}^{\text{o}}\end{array}$

Therefore, the angle $\angle 5$ is ${120}^{\text{o}}$ .

  $6.$

In the first block, draw an inner circle. And the circle is divided into ${360}^{\text{o}}$ .

Now, split the circle into $6$ parts.

Calculate the angle $\angle 6$ ,

  $\begin{array}{l}m\angle 6=\frac{{360}^{\text{o}}}{6}\\ m\angle 6={60}^{\text{o}}\end{array}$

Therefore, the angle $\angle 6$ is ${60}^{\text{o}}$ .