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McGraw-Hill Math Grade 7 Answer Key Lesson 25.2 Types of Angles
Exercises
IDENTIFY
Question 1.
What is the measure of angle Q?
Answer:
50°
Explanation:
The sum of the two angles are 180 degrees.
So, ∠Q = 90° – 40° = 50°
Question 2.
What is the measure of angle Z?
Answer:
103°
Explanation:
The sum of two angles are 180°
∠A = 77°
So, ∠Z = 180° – 77° = 103°
Question 3.
Identify the supplementary angles in the figure below.
Answer:
∠T and ∠V; ∠T and ∠S; ∠S and ∠X; ∠X and ∠V
Explanation:
Two angles are called supplementary when their measures add up to 180 degrees.
Question 4.
The measure of ∠G is given. Determine the measure of the remaining angles.
Answer:
∠F = 120°; ∠E = 60°; ∠H = 120°
Explanation:
Two angles are called supplementary when their measures add up to 180 degrees.
∠G = 60°
So, ∠F = 180° – 60° = 120°
∠E = 180° – 120° = 60°
∠H is opposite of ∠F
So, ∠H = 120°
SOLVE
Question 1.
From this figure, give examples of two complementary, two supplementary, and two vertical angles.
Complementary _______________
Supplementary _____________
Vertical ______________
Answer:
Complementary angles are ∠BGC and ∠BGA; ∠FGE and ∠DGE.
Supplementary angles are ∠BCG and ∠BGF; ∠AGC and ∠AGF; ∠BGA and ∠AGE.
Vertical angles are ∠BGC and ∠FGE; ∠DGC and ∠AGF; ∠AGB and ∠DGE.
Explanation:
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 that are opposite of each other when two lines cross.
Vertical angles are always congruent.
Question 2.
For the figure below, list all complementary and supplementary angles.
Complementary _______________
Supplementary _____________
Answer:
Complementary angles are ∠DFE and ∠CFD; ∠CFB and ∠AFB.
Supplementary angles are ∠AFB and ∠EFB; ∠AFC and ∠CFE; ∠DFE and ∠DFA.
Explanation:
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, they form a right angle.
Explanation:
When we add two angles, there sum should be 90°,
∠DOB + ∠DOC = ∠COB
Given, ∠DOB = 40° and ∠COB = 90°
∠DOC = 90° – 40° = 50°
So, the given angles are complementary angles.
Question 4.
Identify the measure of the angles in this figure.
COD ______________
COF ______________
FOY ______________
YOX ______________
FOX ______________
Answer:
COD = 50°
COF = 90°
FOY = 40°
YOX = 50°
FOX = 90°
Explanation:
The measure of angles formed by the two rays at a common vertex.
Angles are measured in degrees.
When we add two angles, there sum should be 90°,
∠DOB + ∠DOC = ∠COB
Given, ∠DOB = 40° and ∠COB = 90°
∠DOC = 90° – 40° = 50°
∠COF = 90°
∠DOB = 40° and ∠DOC = 50°
∠FOY = 40° and ∠YOX = 90°
∠FOY + ∠YOX = ∠FOX
40° + 50° = 90°