Lesson III. Kinds of Angles

^{Image Source}

Kinds of angles according to their measures:

1.) Acute angle is an angle whose measure is less than 90°.

e.g.

• 5°, 27°, 89°, 15.5°

 2. ) Right angle is an angle whose measure is 90°.

 3. ) Obtuse angle is an angle whose measure is greater than 90°.

e.g.

• 91°, 120°, 100°, 121°.

Kinds of angle pairs:

 1. ) Complementary pair

Complementary pair of angles are two angles whose sum of their measures is 90°.

e.g.

• 20° and 70°, 50° and 40°, 10° and 80°
• The complement of 30° is 60°.
• 15° and 75° are complementary angles.

 2. ) Supplementary pair

Supplementary pair of angles are two angles whose sum of their measures is 180°.

e.g.

• 60° and 120°, 100° and 80°, 110° and 70°
• The supplement of 30° is 150°.
• Two right angles are supplementary.

 3. ) Vertical angles

Vertical angles are two opposite angles formed by intersecting lines or ray.

Line m and line r intersect, forming two pairs of vertical angles.

• ∠1 and ∠3 are vertical pair of angles.
• ∠2 and ∠4 are also pair of vertical angles.

Vertical angles are congruent, therefore:

• ∠1 ≅ ∠3 ; angle 1 is congruent to angle 3.
• ∠2 ≅ ∠4 ; angle 2 is congruent to angle 4.




 4. ) Linear pair

Linear pair of angles are two angles about a point on a straight line.

Note:

Linear pairs are always supplementary.









∠2 and ∠5 are two angles about point B and a common side along line AC.

Therefore ∠2 and ∠5 are vertical angles and m∠2 + m∠5 = 180°




Angles formed by Parallel Lines and its Transversal




A transversal line is a line that cuts two parallel lines at different points.




Given: m || p with u as transversal.


• Vertical angle pairs in the figure:
   ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8
• Linear pairs:
   ∠1 and ∠2, ∠2 and ∠3, ∠5 and ∠6, ∠6 and ∠7
   ∠1 and ∠4, ∠3 and ∠4, ∠5 and ∠8, ∠7 and ∠8
• Alternate-interior angles:
   ∠3 and ∠5, ∠4 and ∠6
• Alternate-exterior angles:
   ∠1 and ∠7, ∠2 and ∠8









Answer the following:

 1. ) Are two right angles supplementary? Why?

 2. ) How many right angles do we have? Why?

 3. ) If ∠A and ∠B are congruent and complementary, what is the measure of ∠A? Why?

 4. ) What is the measure of ∠C if it is a linear pair of 80°?

 5. ) If two angles are complementary but one angle is twice as large as its pair, what are the measures of these angles?







References:
• Grolier International Encyclopedia Vol. 9, Copyright 1991
• The New Book of Popular Science Vol. 1, Copyright 1992









Lessons 4, 5 and 6 will be posted next week!




❤❤❤