Lines and Angles | IT

Question 18

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

Solution

Understand the Question

To measure $\angle \text{AOB}$ $∠ AOB$ using a protractor:
- Align the center point of the protractor with the vertex $O$ .
- Align the base ray $\text{OB}$ with the $0^\circ$ line on the protractor scale.
- Read the degree mark where the second ray $\text{OA}$ intersects the same scale.

Step 1 · Align the Protractor

Align the center of the protractor at vertex $O$ and align ray $\text{OB}$ with the $0^\circ$ mark on the outer scale. Diagram 1

Step 2 · Read the Angle Measure

Follow the outer scale to where ray $\text{OA}$ crosses.

Ray $\text{OA}$ aligns exactly halfway between $80^\circ$ and $90^\circ$ (at the 5th division after $80^\circ$ ).

$\text{Measure of } \angle \text{AOB} = 85^\circ$

Answer

$85^\circ$

Common Mistakes

Reading the Wrong Scale: Protractors have both an inner and an outer scale. Always use the scale that starts with $0^\circ$ on the base ray $\text{OB}$ .
Miscounting Tick Marks: Misreading the halfway mark between $80^\circ$ and $90^\circ$ as $95^\circ$ or $75^\circ$ instead of $85^\circ$ .

More questions in IT

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Q. Can we use this to find out if this angle is greater than, or equal to or smaller than the angle made by the second crane?

Q10

Let us place the circle on the angle made by the second crane so that the vertex coincides with the centre of the circle and one of the arms passes through $OA$ .

Q. Can you now tell which angle is bigger?

Q11

Which crane was making the bigger angle?

If you can make a circular piece of transparent paper, try this method to compare the angles in Fig. 2.10 with each other.

Q12

Is it possible to draw $\overrightarrow{OC}$ such that the two angles are equal to each other in size?

Q13

If a straight angle is formed by half of a full turn, how much of a full turn will form a right angle?

Q14

Angles are classified in three groups as shown below. Right angles are shown in the second group. What could be the common feature of the other two groups?

Q15

What is the measure of a straight angle in degrees? A straight angle is half of a full turn. As a full-turn is $360^\circ$ , a half turn is $180^\circ$ . What is the measure of a right angle in degrees? Two right angles together form a straight angle. As a straight angle measures $180^\circ$ , a right angle measures $90^\circ$ .

Q16

The circle has been divided into 1, 2, 3, 4, 5, 6, 8, 9 10 and 12 parts below. What are the degree measures of the resulting angles? Write the degree measures down near the indicated angles.

Q17

There are two sets of numbers on the protractor: one increasing from right to left and the other increasing from left to right. Why does it include two sets of numbers?

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?

Q20

Measure all three angles of the triangle shown in Fig. 2.21 (a), and write the measures down near the respective angles. Now add up the three measures. What do you get? Do the same for the triangles in Fig. 2.21 (b) and (c). Try it for other triangles as well, and then make a conjecture for what happens in general! We will come back to why this happens in a later year.

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 $\angle \text{SET}$ .