Case Based Questions: Lines and Angles

Q1: Read the source and answer the question that follows

Kabir organized a fun classroom challenge during the mathematics exhibition where students had to guess the angles formed between the hour and minute hands of a clock at different times. He asked everyone to calculate the exact angle at specific hours without using a protractor. For example, at 2:00 PM, the angle formed is x°, and at 4:00 PM, the angle formed is y°.

Q1. Find the values of x and y.
Ans. 60° , 120°
Explanation: 
At 2:00 PM: 
Angle = 2 × 30° = 60° 
At 4:00 PM: 
Angle = 4 × 30° = 120°

Q2.Which angle is greater?
Ans. 120° > 60°, so angle at 4:00 PM is greater

Q3.Are both angles acute, right, or obtuse? 
Ans. 60° = acute ,120° = obtuse

Q4.Draw and label both clock faces showing the angles.  
Ans.

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Q2: Read the source and answer the question that follows

Joy learns the art of knitting from his grandmother.

Q1. Which of the following pictures can be an example of a line segment?

Ans. Option (b) is correct

Q2. How many lines can pass through a point?
Ans. Infinite lines

Q3. Which of the following is an open curve?

Ans. Option(b) is correct

Q3: Read the source and answer the question that follows

In a school science lab, students were conducting an experiment related to angles and light. To observe the effect of sunlight, a window shade was initially pulled open, forming an angle of 95° with the wall. As the intensity of light needed to be increased, the shade was pulled further, creating a larger obtuse angle of 185°. This setup helped students understand how angles can influence light entry.

Q1.  What types of angles are these?
Ans. 95° = obtuse, 185° = reflex

Q2. How many degrees was the increase?
Ans. Change in angle = 185° - 95° = 90°

Q3. Draw both positions of the shade.
Ans. Draw two diagrams with same vertex and two different rays showing each position

Q4. What type of angle will it be if the shade turns 270°?
Ans. If the shade turns 270°, the angle = reflex angle