When two lines are parallel lines are cut by a third line, the angles in corresponding positions are equal in size.
Find the unknown angle measures.
Problem 1 :
Solution :
Angle c and 103 are in corresponding positions. So, they are equal.
∠c = 103
Problem 2 :
Solution :
Angle 130 and b are in corresponding positions. So, they are equal.
∠b = 103
Problem 3 :
Solution :
Angles y and x are in corresponding positions.
y = x
x and 39° are vertically opposite angles.
x = 39° (Vertically opposite angles)
y = 39° (Corresponding angles)
Problem 4 :
Solution :
120 and a° are linear pair.
120 + a = 180
a = 180 - 120
a = 60
a and b are in corresponding positions.
a = b = 60
Problem 5 :
Solution :
Angles x° and 146° are in corresponding positions.
x = 146°
Angles x and y are in corresponding positions.
x = y = 146°
Problem 6 :
Solution :
Angles a and 125 are linear pairs.
a + 125 = 180
a = 180 - 125
a = 55°
b and a are in corresponding positions.
a = b = 55°
Problem 7 :
Solution :
a = 120°, because they are vertically opposite angles.
a = b, because they are corresponding angles.
b and c are linear pair. So,
b + c = 180
120 + c = 180
c = 180 - 120
c = 60°
Again c and d are corresponding angles. So, c = d = 60°
Problem 8 :
Solution :
In the triangle given above,
a and 80° corresponding angles.
So, a = 80°
In the triangle, the sum of interior angles of triangle is 180°.
50 + a + b = 180
50 + 80 + b = 180
130 + b = 180
b =180 - 130
b = 50
Problem 9 :
Solution :
Angles a and 65° are in corresponding positions.
a = 65°
In the triangle,
75 + a + c = 180
75 + 65 + c = 180
140 + c = 180
c = 180 - 140
c = 40
65 + b + c = 180 (linear pair)
65 + b + 40 = 180
105 + b = 180
b = 180 - 105
b = 75
Problem 10 :
Solution :
We have two parallel sides, so one of the angle measure inside the small triangle is 50.
70 + a + 50 = 180
120 + a = 180
a = 180 - 120
a = 60
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM