Solutions: Section 2.6 (Comparing Angles)

Page 20

Q. Is it always easy to compare two angles? Answer: No, it is not always easy to compare two angles (like $89^\circ$ and $91^\circ$) without measuring or overlapping (superimposition). However, for obviously different sizes, comparison is easy.

Figure it Out (Page 23)

Q1. Fold a rectangular sheet of paper, then draw a line along the fold created… Compare angles.

Solution:

• Angles formed: $\angle AEF, \angle BEF, \angle DFE, \angle CFE$.
• $\angle AEF$ and $\angle CFE$ are larger than $\angle BEF$ and $\angle DFE$ in standard oblique folds.
• (Activity based: Try folding rectangular sheets in different ways).

Q2. In each case, determine which angle is greater and why.

• a. $\angle AOB$ or $\angle XOY$
• b. $\angle AOB$ or $\angle XOB$
• c. $\angle XOB$ or $\angle XOC$

Solution:

• (a) $\angle AOB$ is greater. $\angle XOY$ is an acute angle contained within $\angle AOB$.
• (b) $\angle AOB$ is greater (it contains $\angle XOB$).
• (c) None. $\angle XOB$ is the same as $\angle XOC$ if $B$ and $C$ are on the same ray.

Q3. Which angle is greater: $\angle XOY$ or $\angle AOB$?

Solution:

• By simply looking at the figure, it might be hard to say. Superimposition or measurement is necessary to be exact.