A line is an infinite number of points between two end points. Where two lines meet or cross, they form an angle.
An angle is an amount of rotation. It is measured in degrees.
Adjacent angles :
Angle that have common vertex and a common arm.
Adjacent angles on a straight line add upto 180 degree.
Perpendicular lines :
Lines that meet or cross at 90°
Here AB ⊥ CD.
Vertically opposite angles :
When two straight lines intersect the angles opposite each other are called vertically opposite angles.
Vertically opposite angles are equal to each other.
Transversals creates three important types of angles, namely:
1. Corresponding angles
2. Co-interior angles
3. Alternating angles
Corresponding angles are in the same position as each other.
Co-interior angles are between the lines and on the same side of the transversal. They are “inside together”.
Alternate angles are between the lines and on alternate (opposite) sides of the transversal.
Problem 1 :
Find the value of each variable, providing reasons for your statements:
Solution :
Reason :
Vertically opposite angles are equal.
x = 95°
Problem 2 :
Solution :
Reason :
x and 145 are linear pairs.
x + 145 = 180
x = 180 - 145
x = 35°
Problem 3 :
Solution :
Reason :
40 and x add upto 90 degree.
40 + x = 90
x = 90 - 40
x = 50°
Problem 4 :
Solution :
Reason :
50°, 60° and x are supplementary angles.
50° + 60° + x = 180°
110° + x = 180°
x = 180° - 110°
x = 70°
x, y and z are supplementary angles.
x + y + z = 180
Applying the value of x, we get
70 + y + z = 180
y + z = 110
So, x = 70°, y = 50° and z = 60°
Problem 5 :
Solution :
Reason :
x and y are right angles.
x = 90° and y = 90°
Problem 6 :
Solution :
Reason :
70° and x + 20° are vertically opposite angles.
70° = x + 20°
70° - 20° = x
x = 50°
Problem 7 :
Solution :
Reason :
140° and 3x - 10 are supplementary angles.
140 + 3x - 10 = 180
130 + 3x = 180
3x = 180 - 130
3x = 50
x = 50/3°
Problem 8 :
Solution :
Since the lines AB and CD are parallel, 108 and x are corresponding angles.
Reason :
x and y are supplementary.
x = 108
x + y = 180
108 + y = 180
y = 180 - 108
y = 72
Problem 9 :
Solution :
Reason :
x and 88° are vertically opposite angles.
Since the lines EF and HG are parallel, x and y are corresponding angles.
x = 88 and y = 88.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM