McGraw Hill Math Grade 8 Lesson 19.3 Answer Key Finding Missing Angle Measurements

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McGraw-Hill Math Grade 8 Answer Key Lesson 19.3 Finding Missing Angle Measurements

Exercises

SOLVE

Question 1.
Fill in the angle measurements for the other seven angles.

∠a = _________
∠b = _________
∠c = _________
∠d = _________
∠e = _________
∠f = _________
∠g = _________
Answer:
∠a = 108⁰, 
∠b = 72⁰,
∠c = 108⁰,
∠d = 72⁰,
∠e = 108⁰, 
∠f =  72⁰, 
∠g = 108⁰,
∠h = 72⁰, 

Explanation:
Given ∠h = 72⁰, As ∠e = 180⁰ – 72⁰ = 108⁰, 
∠h = 72⁰ = ∠f = 72⁰, ∠g = 180⁰ – 72⁰ = 108⁰, ∠e = ∠a = 108⁰,
 ∠b = 180⁰ – 108⁰ = 72⁰,  ∠c = ∠g = 108⁰, ∠d = 180⁰ – 108⁰ = 72⁰.
Therefore ∠a = 108⁰,  ∠b = 72⁰, ∠c = 108⁰, ∠d = 72⁰,
∠e = 108⁰,  ∠f =  72⁰,  ∠g = 108⁰, ∠h = 72⁰..

Question 2:
Angle 3 is 48 degrees. List the measurements of the other seven angles.

∠1 = _________
∠2 = _________
∠3 = _________
∠4 = _________
∠5 = _________
∠6 = _________
∠7 = _________
Answer:
∠1 = 48⁰, 
∠2 = 132⁰,
∠3 = 48⁰,
∠4 = 132⁰,
∠5 = 48⁰, 
∠6 =  132⁰, 
∠7 = 48⁰,
∠8 = 132⁰, 

Explanation:
Given ∠3 = 48⁰, As ∠4 = 180⁰ – 48⁰ = 132⁰, 
∠1 = ∠3 = 48⁰, ∠2 = 180⁰ – 48⁰ = 132⁰,
∠5 = ∠1 = 48⁰,  ∠6 = 180⁰ – 48⁰ = 132⁰,
 ∠7 = ∠3 = 48⁰, ∠8 = 180⁰ – 108⁰ = 132⁰.
Therefore ∠1 = 48⁰,  ∠2 = 132⁰, ∠3 = 48⁰, ∠4 = 132⁰,
∠5 = 48⁰,  ∠6 =  132⁰,  ∠7 = 48⁰, ∠8 = 132⁰, 

Question 3.

Fill in the angle measurements for the other seven angles.
∠a = _________
∠b = _________
∠c = _________
∠d = _________
∠e = _________
∠g = _________
∠h = _________
Answer:
∠a = 125⁰, 
∠b = 55⁰,
∠c = 125⁰,
∠d = 55⁰,
∠e = 125⁰, 
∠g = 125⁰,
∠h = 55⁰, 

Explanation:
Given ∠f = 55⁰, So ∠g = 180⁰ – 55⁰ = 125⁰, 
∠g = ∠e = 125⁰, ∠h = 180⁰ – 125⁰ = 55⁰,
∠e = ∠a = 125⁰,  ∠b = 180⁰ – 125⁰ = 55⁰,  ∠c = ∠g = 125⁰,
∠d = 180⁰ – 125⁰ = 55⁰.
Therefore ∠a = 125⁰,  ∠b = 55⁰, ∠c = 125⁰, ∠d = 55⁰,
∠e = 125⁰,  ∠g = 125⁰, ∠h = 55⁰,

Question 4.

What is the measurement of ∠FOE? ______________
What is the measurement of ∠EOC? ______________
What is the measurement of ∠BOC? ______________
Answer:
The measurement of ∠FOE is 46⁰,
The measurement of ∠EOC is 90⁰,
The measurement of ∠BOC is 45⁰,

Explanation:
Given figure the measurement of ∠FOE is 46⁰ as
∠EOG = 90⁰ and given ∠FOG = 44⁰ , so therefore
∠FOE = ∠EOG – ∠FOG = 90⁰ – 44⁰ = 46⁰.
The measurement of ∠EOC is 90⁰ as ∠EOC = ∠EOG = 90⁰.
Now the measurement of ∠BOC is 45⁰ as ∠COA = 90⁰ = ∠AOB  + ∠BOC,
So ∠BOC = 90⁰ – ∠AOB  = 90⁰ – 45⁰ = 45⁰.