McGraw Hill Math Grade 8 Lesson 19.2 Answer Key Types of Angles: Supplementary, Complementary, Interior, and Exterior

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McGraw-Hill Math Grade 8 Answer Key Lesson 19.2 Types of Angles: Supplementary, Complementary, Interior, and Exterior

Exercises

IDENTIFY

Question 1.
From the figure below, give examples of two complementary, two supplementary and two vertical angles.
Complementary ________________
Supplementary ________________
Vertical ________________

Answer:
Complementary angles are CD, FG,
Supplementary angles are AD, CF,
Vertical angles are BE, AD,

Explanation:
Complementary: Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees. Vertical angles are angles opposite each other where two lines cross.
Vertical angles are angles that are opposite each other when two lines intersect
each other. The two pairs of opposite angles are equal to each other.
The two pairs of neighboring angles are supplementary, meaning they
add up to 180 degrees. Therefore given Complementary angles are CD,
FG, Supplementary angles are AD, CF, Vertical angles are BE, AD.

Question 2.
For the figure below, list all complementary and supplementary angles.

Complementary ________________
Supplementary ________________
Answer:
Complementary angles : Angle AC, Angle CE,
Supplementary: Angle AE or Angle EA,

Explanation:
Complementary: Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Question 3.

Are angle DOB and angle DOC complementary? Explain.
Answer:
Yes, Complementary,

Explanation:
Yes angle DOB and angle DOC are complementary as there sum of angles of
DOB and DOC  is 90 degrees.

Question 4.
In the figure below, a line is intersecting two parallel lines. Fill in the missing information:

∠a = ∠_________ = ∠_________ = ∠___________
Answer:
∠a = ∠e = ∠d = ∠h,

Explanation:
The missing information a line is intersecting two parallel lines are
∠a = ∠e = ∠d = ∠h.

Question 5.
In the figure below, a line is intersecting two parallel lines. Fill in the missing angle measurements:

∠a = _________;
∠b = _________;
∠c = _________;
∠d = _________;
∠e = _________;
∠f = _________;
∠h = _________;
Answer:
∠a = 125 degrees;
∠b = 55 degrees;
∠c = 125 degrees;
∠d = 55 degrees;
∠e = 125 degrees;
∠f = 55 degrees;
∠g= 125 degrees,
∠h = 55 degrees,

Explanation:
Given line is intersecting two parallel lines. The missing angle measurements are
∠a = 125 degrees;
∠b = 55 degrees;
∠c = 125 degrees;
∠d = 55 degrees;
∠e = 125 degrees;
∠f = 125 degrees;
∠h = 55 degrees as ∠a  + ∠b = 180 degrees,
∠c + ∠d = 180 degrees and ∠d = 55 degrees so ∠c = 180 – 55 = 125 degrees,
as ∠a = ∠c = 125 degrees, ∠b = 180 – 125 = 55 degrees,
∠e + ∠f = 180 degrees,
∠g + ∠h = 180 degrees and ∠g = 125 degrees so ∠h = 180 – 125 = 55 degrees,
as ∠e = ∠g = 125 degrees, ∠f = 180 – 125 = 55 degrees,