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30 Sep 2021, 05:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
56% (02:01) correct
44%
(01:58)
wrong
based on 62
sessions
History
Date
Time
Result
Not Attempted Yet
What is the measure of \(\angle A\)
I. \(100<A<130\)
II. \(50<A<80\)
III. \(90<A<125\)
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
Attachment:
1.jpg [ 22.42 KiB | Viewed 2370 times ]
30 Sep 2021, 17:56
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Correct Option D
I and III - Angle CGE ranges from 90 to 130.
Correct Angle is 120.
Method 1.
Property 1
Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees (straight line)
Line ADF is a straight line: angle EDC + angle CDF = 180°
Angle EDC = 180° - 80° = 120°
Property 2: opposite angle of parallelogram are Equal
Angle A = Angle EDC = 120°
Angle A = 120°
Method 2:
Property 1 : Vertical angles are a pair of opposite angles formed by intersecting lines.
Angle CDF = Angle EDB = 80°
Property 2 : Sum of all angle in triangle must be equal to 180°
Angle DEB + Angle EDB + Angle DBE = 180°
40° + 80° + Angle DBE = 180
Angle DBE = 180° - 120° = 60°
Angle DBE = 60°
Property 3 : Sum of quadrilateral opposite angle is 180°
Angle A + Angle DBE = 180°
Angle A = 180 - 60° = 120°
Angle A = 120°
Method 3
Property 1
When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles
Angle CDE = 120°
Angle GED = 180° - 120° = 60° - consecutive interior angles.
Angle A + Angle GED = 180
Angle A = 180° - 60° = 120°
Angle A = 120°
Posted from my mobile device
I and III - Angle CGE ranges from 90 to 130.
Correct Angle is 120.
Method 1.
Property 1
Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees (straight line)
Line ADF is a straight line: angle EDC + angle CDF = 180°
Angle EDC = 180° - 80° = 120°
Property 2: opposite angle of parallelogram are Equal
Angle A = Angle EDC = 120°
Angle A = 120°
Method 2:
Property 1 : Vertical angles are a pair of opposite angles formed by intersecting lines.
Angle CDF = Angle EDB = 80°
Property 2 : Sum of all angle in triangle must be equal to 180°
Angle DEB + Angle EDB + Angle DBE = 180°
40° + 80° + Angle DBE = 180
Angle DBE = 180° - 120° = 60°
Angle DBE = 60°
Property 3 : Sum of quadrilateral opposite angle is 180°
Angle A + Angle DBE = 180°
Angle A = 180 - 60° = 120°
Angle A = 120°
Method 3
Property 1
When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles
Angle CDE = 120°
Angle GED = 180° - 120° = 60° - consecutive interior angles.
Angle A + Angle GED = 180
Angle A = 180° - 60° = 120°
Angle A = 120°
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