GSEB Class 6 Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.4

Question 1. What is the measure of
(i) a right angle? and
(ii) a straight angle?

Answer:
(i) The measure of a right angle is 90 degrees.
(ii) The measure of a straight angle is 180 degrees.
In simple words: A right angle is always 90 degrees, and a straight angle is always 180 degrees.

Exam Tip: Focus on fundamental angle definitions for quick recall and to avoid common mistakes.

Question 2. Say true or false:
(a) The measure of an acute angle \( < 90^\circ \)
(b) The measure of an obtuse angle \( < 180^\circ \)
(c) The measure of a reflex angle \( > 180^\circ \)
(d) The measure of one complete revolution \( = 360^\circ \).
(e) If \( m\angle A = 53^\circ \) and \( m\angle B = 35^\circ \), then \( m\angle A > m\angle B \).

Answer:
(a) True (An acute angle is always less than 90 degrees.)
(b) False (An obtuse angle is greater than 90 degrees but less than 180 degrees.)
(c) True (A reflex angle always measures more than 180 degrees.)
(d) True (A full rotation equals 360 degrees.)
(e) True (Since 53 degrees is larger than 35 degrees, this statement is correct.)
In simple words: Understand the rules for each angle type. Acute angles are small, obtuse angles are medium-sized, reflex angles are big, and a full circle is 360 degrees. Then compare numbers directly to tell if one is bigger.

Exam Tip: Remember the precise definitions and value ranges for each type of angle to avoid common mistakes, especially for obtuse and reflex angles.

Question 3. Write down the measures of
(a) some acute angles and
(b) some obtuse angles.
(Give at least two examples of each)

Answer:
(a) For acute angles, some good examples are \( 63^\circ \) and \( 72^\circ \).
(b) For obtuse angles, you could use \( 120^\circ \) and \( 100^\circ \) as examples.
In simple words: Pick any angles smaller than 90 degrees for acute, and any angles between 90 and 180 degrees for obtuse. Just show two for each.

Exam Tip: Acute angles are smaller than 90 degrees, while obtuse angles are larger than 90 degrees but smaller than 180 degrees. Provide diverse examples within these ranges.

Question 4. Measure the angles given below using the protractor and write down the measure.

Answer: The measures for the given angles are as follows:
(a) \( 45^\circ \)
(b) \( 125^\circ \)
(c) \( 90^\circ \)
(d) \( \angle 1 = 60^\circ \)
(d) \( \angle 2 = 125^\circ \)
(d) \( \angle 3 = 90^\circ \)
In simple words: Use a protractor to find the exact number of degrees for each angle in the pictures.

Exam Tip: Practice using a protractor carefully; aligning the base line and vertex is crucial for accurate angle measurements. Be specific if an image contains multiple angles.

Question 5. Which angle has a large measure? First estimate and then measure.

Answer: After measuring, we found that Angle A is \( 40^\circ \), and Angle B is \( 65^\circ \).
Therefore, \( \angle B > \angle A \). Angle B has a larger size compared to Angle A.
In simple words: We checked the angles. Angle B was bigger than Angle A.

Exam Tip: Visual estimation can be a helpful first step, but always confirm with precise measurement using a protractor to ensure accuracy.

Question 6. From these two angles which has larger measure? Estimate and then confirm by measuring them.

Answer: Visually, Angle 2 appears bigger than Angle 1.
Upon measuring, Angle 1 is \( 45^\circ \), and Angle 2 is \( 60^\circ \).
This shows that Angle 2 has the greater size.
In simple words: We looked at the angles and thought Angle 2 was bigger. After measuring, Angle 2 was indeed bigger than Angle 1.

Exam Tip: Always compare both estimated and measured values; practice helps improve estimation skills over time. Clearly state both your estimate and your confirmed measurement.

Question 7. Fill in the blanks with acute, obtuse, right or straight:
(a) An angle whose measure is less than that of a right angle is ........................................
(h) An angle whose measure is greater than that of a right angle is ........................................
(c) An angle whose measure is the sum of the measures of two right angles is ........................................
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is ........................................
(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be ........................................

Answer:
(a) acute angle.
(b) obtuse angle.
(c) straight angle.
(d) acute angle.
(e) obtuse angle.
In simple words: Fill in the blanks with the correct angle type based on its definition or how it relates to other angles.

Exam Tip: Understand the properties of acute, obtuse, right, and straight angles to accurately fill in these types of blanks. A right angle is \( 90^\circ \), and a straight angle is \( 180^\circ \).

Question 8. Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor)

Answer: The measures for each angle shown are:
(i) The angle measures \( 40^\circ \).
(ii) The angle measures \( 130^\circ \).
(iii) The angle measures \( 65^\circ \).
(iv) The angle measures \( 135^\circ \).
In simple words: Look at each picture, guess the angle, then use your protractor to get the real number for each one.

Exam Tip: Always estimate before measuring; this helps develop a better intuitive understanding of angle sizes and makes it easier to spot measurement errors.

Question 9. Find the angle measure between the hands of the clock in each figure:

Answer: The angles formed by the clock hands are:
(i) At 9:00 a.m., the angle is \( 90^\circ \).
(ii) At 1:00 p.m., the angle is \( 30^\circ \).
(iii) At 6:00 p.m., the angle is \( 180^\circ \).
In simple words: For each clock face, figure out the angle between the two clock hands.

Exam Tip: Remember that a full clock face is \( 360^\circ \), and there are 12 hours. This means each hour mark represents \( 360/12 = 30^\circ \) of angle.

Question 10. Investigate in the given figure, the angle measures \( 30^\circ \). Look at the same figure through a magnifying glass. Does the angle becomes larger ? Does the size of the angle change ?

Answer: No, observing an angle through a magnifying glass does not make its actual measure larger.
The size of the angle does not change; only its visual appearance is magnified.
In simple words: A magnifying glass makes things look bigger, but it does not change their actual size or how many degrees an angle has.

Exam Tip: A magnifying glass changes the *apparent* size of an object, but not its true dimensions or angular measure. Physical properties remain unchanged.

Question 11. Measure and classify each angle:

Answer: After measuring each of these angles, we obtained the following values: \( \angle AOB \) is \( 40^\circ \), \( \angle AOC \) is \( 125^\circ \), \( \angle BOC \) is \( 85^\circ \), \( \angle DOC \) is \( 95^\circ \), \( \angle DOA \) is \( 140^\circ \), and \( \angle DOB \) is \( 180^\circ \). We can then fill in the table below to classify each one:

Exam Tip: Always double-check your angle measurements and recall the definitions for acute (less than \( 90^\circ \)), obtuse (between \( 90^\circ \) and \( 180^\circ \)), right (exactly \( 90^\circ \)), and straight (exactly \( 180^\circ \)) angles. A table helps to organize your answers clearly.