write the five different types of special pairs of angles and define the one by one
Answers
Answer:
The following diagrams show how vertical angles, corresponding angles, and alternate angles are formed. Scroll down the page for more examples and solutions.
vertical angles, corresponding angles, alternate angles
Complementary Angles
Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees (right angle). One of the complementary angles is said to be the complement of the other.
The two angles do not need to be together or adjacent. They just need to add up to 90 degrees. If the two complementary angles are adjacent then they will form a right angle.
complementary angle
∠ABC is the complement of ∠CBD
Supplementary Angles
Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees (straight line) . One of the supplementary angles is said to be the supplement of the other.
The two angles do not need to be together or adjacent. They just need to add up to 180 degrees. If the two supplementary angles are adjacent then they will form a straight line.
supplementary angles
∠ABC is the supplement of ∠CBD
Vertical Angles
Two pairs of angles are formed by two intersecting lines. Vertical angles are opposite
angles in such an intersection. Vertical angles are equal to each other.
vertical angles
Very often math questions will require you to work out the values of angles given in diagrams by applying the relationships between the pairs of angles.
Example 1: Given the diagram below, determine the values of the angles x, y and z.
vertical angles
Solution:
Step 1:
x is a supplement of 65°.
Therefore, x + 65° =180° ⇒ x = 180° – 65° = 115°
Step 2:
z and 115° are vertical angles.
Therefore, z = 115°
Step 3:
y and 65° are vertical angles.
Therefore, y = 65°
Answer:
x = 115°, y = 65° and z = 115°