3 Marks Question

Question 13 Marks

Estimate the size of each angle and then measure it with a protractor:

Classify these angles as acute, right, obtuse or reflex angles.

Answer

(a) $45^{\circ}$ acute
(b) $150^{\circ}$ obtuse
(c) $120^{\circ}$ obtuse
(d) $30^{\circ}$ acute
(e) $95^{\circ}$ obtuse
(f) $350^{\circ}$ reflex

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Question 23 Marks

In each of the below grids, join A to other grid points in the figure by a straight line lo get:

Mark the intended angles with curves to specify the angles. One has been done for you.

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Question 33 Marks

Angles in a clock:
(a) The hands of a clock make different angles at different times. At 1 o’clock, the angle between the hands is $30^{\circ}$ Why?
(b) What will be the angle at 2 o’clock? And at 4 o’clock? 6 o’clock?
(c) Explore other angles made by the hands of a clock.

Answer

(a) Numbers 1 to 12 are written along the circumference of a clock at equal distances. 360 ÷ 12 = 30.
Hence, angle between two consecutive numbers is $30^{\circ}$
At $1^{\circ \prime}$ clock hands are at 0 and 1 (consecutive numbers)
Hence angle between them is $30^{\circ}$.
(b) Angle between hands at $2 o^{\circ}$ clock $=2 \times 30^{\circ}=60^{\circ}$ angle between hands at 4 o $^{\prime}$ clock $=4 \times 30^{\circ}=120^{\circ}$
Angle between hands at $6 o^{\prime}$ clock $=6 \times 30^{\circ}=180^{\circ}$
(c) Angle between hands at $5o^{\prime}$ clock $=5 \times 30^{\circ}=150^{\circ}$
Angle between hands at $7 o^{\prime}$ clock $=7 \times 30^{\circ}=210^{\circ}$
Angle between hands at $8 o^{\prime}$ clock $=8 \times 30^{\circ}=240^{\circ}$

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Question 43 Marks

Measure and write the degree measures for each of the following angles:

Answer

(a) Measure of given angle is $80^{\circ}$
(b) Measure of given angle is $120^{\circ}$
(c) Measure of given angle is $60^{\circ}$
(d) Measure of given angle is $130^{\circ}$
(e) Measure of given angle is $130^{\circ}$
(f) Measure of given angle is $60^{\circ}$

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Question 53 Marks

Find out the number of acute angles in each of the figures below.

What will be the next figure and how many acute angles will it have? Do you notice any pattern in the numbers?

Answer

First figure There are three acute angles in the first figure.
Second figure There are 12 acute angles in second figure (each of the 4 smaller triangles has 3 acute angles)
Third figure There are 21 acute angles in the third figure (each of the 7 smaller triangles has 3 acute angles).
Explanation As the figure increase in complexity, the number of acute angles increase in a pattern triangles and therefore more acute angles. The pattern shows that the number of acute angles triples with each step.

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