Vertically opposite angles are equal in size.
Find the unknown angles in the following figures.
Problem 1 :
Solution :
Since a and 133 are vertically opposite, they will be equal.
So, ∠a = 133.
Problem 2 :
Solution :
Since c and 52 are vertically opposite, they will be equal.
So, ∠c = 52
Problem 3 :
Solution :
Since b and 73 are vertically opposite, they will be equal.
So, ∠b = 73
Problem 4 :
Solution :
81 = 65 + d
Subtracting 65 on both sides, we get
81 - 65 = d
d = 16
Problem 5 :
Find the value of m.
Solution :
m + 20 = 100
Subtracting 20 on both sides.
m = 100 - 20
m = 80
Problem 6 :
Solution :
3t + 12 = 66
Subtracting 12 on both sides.
3t = 66 - 12
3t = 54
Dividing by 3, we get
t = 54/3
t = 18
Problem 7 :
Find the value of p.
Solution :
2p + 30 = 108
Subtracting 30 on both sides.
2p = 108 - 30
2p = 78
Dividing by 2, we get
p = 78/2
p = 39
Problem 8 :
Find the value of z.
Solution :
58 and 2z - 10 are vertically opposite angles.
58 = 2z - 10
Add 10 on both sides.
68 = 2z
dividing by 2
z = 68/2
z = 34
Problem 9 :
Find the value of y.
Solution :
102 - 2y and 78 are vertically opposite angles.
78 = 102 - 2y
Add 2y on both sides.
2y + 78 = 102
Subtracting 78, we get
2y = 102 - 78
2y = 24
Dividing by 2 on both sides.
y = 24/2
y = 12
Problem 10 :
Find the value of r.
Solution :
126 and 180 - 3r are vertically opposite angles.
126 = 180 - 3r
Add 3r on both sides.
126 + 3r = 180
Subtracting 126 on both sides.
3r = 180 - 126
3r = 54
r = 54/3
r = 18
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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