Solutions: Section 2.10 & 2.11 (Drawing & Classification)

Figure it Out (Page 49 - Text Fig 2.23)

Q1. List all angles possible, guess measures, then measure.

Solution: Angles include: $\angle CAP, \angle ACD, \angle APL, \angle DLP, \angle RPL, \angle SLP, \angle PRS, \angle LSR, \angle BRS, \angle CLP$.

Figure it Out (Page 52 - Text Page 40)

Q2. Use a protractor to find the measure of each angle. Then classify.

Solution:

• a. $\angle PTR = 30^\circ$ (Acute)
• b. $\angle PTQ = 60^\circ$ (Acute)
• c. $\angle PTW = 102^\circ$ (Obtuse)
• d. $\angle WTP = 258^\circ$ (Reflex)

Let’s Explore (Page 53 - Text Page 41)

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

Solution:

• $\angle REB$ is a straight angle ($180^\circ$).
• $\angle BET = 180^\circ - 80^\circ = 100^\circ$.
• $\angle SET = 10^\circ$ (based on diagram context of perpendiculars).

Figure it Out (Page 53 - Text Page 41)

Q3. Make any figure with three acute angles, one right angle and two obtuse angles. Solution: (Drawing task).

Q4. Draw letter ‘M’ with 40 degree sides and 60 degree middle. Solution: (Drawing task).

Q6. Ashoka Chakra:

• Angle between spokes: $360^\circ \div 24 = 15^\circ$.
• Largest acute angle: $75^\circ$ (5 spokes: $5 \times 15 = 75$, 6 spokes = 90 which is right, not acute).

Q7. Puzzle: I am an acute angle.

• $\times 2 =$ Acute
• $\times 3 =$ Acute
• $\times 4 =$ Acute
• $\times 5 =$ Obtuse

Solution: The angle must be between $18^\circ$ and $22.5^\circ$. Possible integer answers: 19°, 20°, 21°, 22°.

• Check 22: $22 \times 4 = 88$ (Acute). $22 \times 5 = 110$ (Obtuse). Correct.
• Check 18: $18 \times 4 = 72$ (Acute). $18 \times 5 = 90$ (Right, not obtuse). Incorrect.