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Answer:
(A)
1= 61° ...(Corresponding angles )
3=1 ...(Vertically opposite angle)
3= 61°
3=6 ...(Corresponding angles)
6=61°
1+2=180° ...(Linear angle)
61°+2=180°
2=180-61
2=119°
2=5 ...(Corresponding angles)
5= 119°
5=7 ...(Vertically opposite angle)
7=119°
4=2 ...(Vertically opposite angle)
4=119°
(B)
2=99° ...(Vertically opposite angle)
2=6 ...(Corresponding angles )
6=99°
6=4 ...(Vertically opposite angle)
4=99°
4+5=180 ...(Linear angle)
99+5=180
5=180-99
5=81°
5=7 ...(Vertically opposite angle)
7=81°
1=5 ...(Corresponding angles )
1=81°
1=3 ...(Vertically opposite angle)
3=81°
This way you can solve (C)
Step-by-step explanation:
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Solution (a) :
Angle 61° = Angle 6 ( They both are vertically opposite angles , which means their angle measure will be equal )
[ Angle 6 = 61° ]
Angle 61° + angle 5 = 180° ( they are a linear pair and the sum of a linear pair is always equal to 180° )
Angle 5 = 180° - 61°
[ Angle 5 = 119° ]
Angle 5 = Angle 7 ( they are vertically opposite angles , which means their angle measure will be equal )
Angle 5 = 119° = angle 7
[ Angle 7 = 119° ]
Angle 4 = angle 5 ( interior opposite angles in a transversal are always equal )
Angle 4 = Angle 5 = 119°
[ Angle 4 = 119° ]
Angle 61° = Angle 3 ( interior opposite angles in a transversal are always equal )
[ Angle 3 = 61° ]
Angle 1 = Angle 3 ( vertically opposite angles in a transversal are equal )
[ Angle 1 = 61° ]
Angle 4 = Angle 2 ( vertically opposite angles in a transversal are equal )
[ Angle 2 = 119° ]
Therefore , angle 1 = 61° , angle 2 = 119° , angle 3 = 61° , angle 4 = 119° , angle 5 = 119° , angle 6 = 61° , angle 7 = 119° .
Solution (b) :
Angle 1 + angle 99° = 180° ( they are a linear pair )
Angle 1 = 180° - 99°
[ Angle 1 = 81° ]
Angle 1 = Angle 3 ( vertically opposite angles in a transversal are equal )
[ Angle 3 = 81° ]
Angle 99° = Angle 2 ( vertically opposite angles in a transversal are equal )
[ Angle 2 = 99° ]
Angle 99° = Angle 4 ( corresponding angles in a transversal are equal )
[ Angle 4 = 99° ]
Angle 1 = Angle 5 ( corresponding angles in a transversal are equal )
[ Angle 5 = 81° ]
Angle 2 = Angle 6 ( corresponding angles in a transversal are equal )
[ Angle 6 = 99° ]
Angle 7 = Angle 3 ( corresponding angles in a transversal are equal )
[ Angle 7 = 81° ]
Therefore , angle 1 = 81° , angle 2 = 99° , angle 3 = 81° , angle 4 = 99° , angle 5 = 81° , angle 6 = 99° and angle 7 =81°.
Solution (c) :
Angle adjacent to angle 1 = 90°
Angle 1 + angle 90° = 180° ( linear pair always sums up to 180° )
Angle 1 = 180 - 90
[ Angle 1 = 90° ]
Angle 1 = Angle 3 ( vertically opposite angles in a transversal are equal )
[ Angle 3 = 90° ]
Angle 90° = Angle 2 ( vertically opposite angles in a transversal are equal )
[ Angle 2 = 90° ]
Angle 3 = Angle 5 ( alternate interior angles in a transversal are equal )
[ Angle 5 = 90° ]
Angle 2 = Angle 4 ( alternate interior angles in a transversal are equal )
[ Angle 4 = 90° ]
Angle 6 = Angle 4 ( vertically opposite angles in a transversal are equal )
[ Angle 6 = 90° ]
Angle 5 = Angle 7 ( vertically opposite angles in a transversal are equal )
[ Angle 7 = 90° ]
Therefore , angle 1 = 90° , angle 2 = 90° , angle 3 = 90° , angle 4 = 90° , angle 5 = 90° , angle 6 = 90° and angle 7 = 90° .
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