Question

answer the following:
(a) Name four pairs of adjacent angles.
(b) Name a linear pair of angles.
(c) Name a pair of non-adjacent complementary and supplementary angles.
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Answer 1

a) Adjacent angles are the angles with a common arm and a common vertex.

• Example 1: Consider an angle ∠ABC = 60°. When this angle is bisected, then they are adjacent angles.
• Example 2: Consider two angles of any degree ∠ABC and ∠CBD. Here both the angles have the same vertex B and common arm BC.
• Example 3: Consider an angle ∠XYZ of 180°. 120° and 60° can be adjacent angles.
• Example 4: Consider an angle ∠QPR of 90°. Any pair of angles that sum up to 90° can be adjacent angles.

b) Linear pair of angles is the adjacent angles which sum up to 180°.

• Examples of linear pair of angles may include 90° and 90°, 120° and 60°, etc.

c) Complementary angles are two angles that add to 90 degrees. Supplementary angles are two angles whose measures add up to 180°.

• Non-adjacent angle: Consider two angles ∠ABC and ∠XYZ. Here both angles have no common vertex and no common arm, so they are non-adjacent angles.
• Complementary angles: 60° and 30°
• Supplementary angles: 160° and 20°