In Fig. 2.19, we have . Why?

Understand the Question A straight angle (semicircle) has a total measure of . The total angle from ray to ray is divided into equal adjacent angles. The value of each angle is found by dividing the total angle () by the number of equal parts (). Step 1 · Identify Total Angle and Number of Parts The line from to forms a straight line/semicircle with a total angle of . Counting the smaller equal angles: There are equal parts. Step 2 · Calculate Each Angle Divide the total angle by the number of equal parts: Answer > (because the total straight angle of is divided into equal parts) Common Mistakes Counting Rays Instead of Angles: Counting rays ( through ) instead of the angle intervals formed between them. Using Instead of : Confusing a straight angle/semicircle () with a full circle ().

Lines and Angles | IT

Question 19

In Fig. 2.19, we have $\angle AOB = \angle BOC = \angle COD = \angle DOE = \angle EOF = \angle FOG = \angle GOH = \angle HOI = \text{______}$ . Why?

Solution

Understand the Question

A straight angle (semicircle) has a total measure of $180^\circ$ .
The total angle from ray $OA$ to ray $OI$ is divided into $8$ equal adjacent angles.
The value of each angle is found by dividing the total angle ( $180^\circ$ ) by the number of equal parts ( $8$ ).

Step 1 · Identify Total Angle and Number of Parts

The line from $OA$ to $OI$ forms a straight line/semicircle with a total angle of $180^\circ$ . Diagram 1

Counting the smaller equal angles: $\angle AOB, \angle BOC, \angle COD, \angle DOE, \angle EOF, \angle FOG, \angle GOH, \angle HOI$

There are $8$ equal parts.

Step 2 · Calculate Each Angle

Divide the total angle by the number of equal parts:

\begin{aligned} 180^\circ \div 8 &= 22.5^\circ \end{aligned}

Answer

$22.5^\circ$ (because the total straight angle of $180^\circ$ is divided into $8$ equal parts)

Common Mistakes

Counting Rays Instead of Angles: Counting $9$ rays ( $OA$ through $OI$ ) instead of the $8$ angle intervals formed between them.
Using $360^\circ$ Instead of $180^\circ$ : Confusing a straight angle/semicircle ( $180^\circ$ ) with a full circle ( $360^\circ$ ).

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Q10

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Q12

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Q13

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Q17

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Q18

What is the degree measure of $\angle \text{AOB}$ ?

Q19

In Fig. 2.19, we have $\angle AOB = \angle BOC = \angle COD = \angle DOE = \angle EOF = \angle FOG = \angle GOH = \angle HOI = \text{______}$ . Why?

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Q21

Let's Explore

In this figure, $\angle \text{TER} = 80^\circ$ . What is the measure of $\angle \text{BET}$ ? What is the measure of $\angle \text{SET}$ ?

Hint: Observe that $\angle \text{REB}$ is a straight angle. Hence, the degree measure of $\angle \text{REB} = 180^\circ$ of which $80^\circ$ is covered by $\angle \text{TER}$ . A similar argument can be applied to find the measure of $\angle \text{SET}$ .