Adjacent angles will have a common vertex and a common side.
The angle near to each other is called as adjacent angle.
Adjacent angle will never overlap.
The pair of opposite angle that is formed by intersection of the two straight lines.
Vertical angles are always equal.
Two pair of vertical angle adds to 360 degree
I like to share this Trig Reference Angles with you all through my article.
Diagram of adjacent vertical angles:
Adjacent angle:
The adjacent angles V and S form the right angle, they are complementary.
Vertical angles :
The vertical angle 1 and angle 2 are equal.
They are always opposite to each other.
Examples for adjacent vertical angles :
Example problems :
Q 1: Find the measure of the angle S. When the angle V is 35 degree and the adjacent angle sum up to 90 degree.
Sol : Angle S +angle V= 90
Angle S +35 = 90
Angle S= 90-35
Angle S = 55
Q 2: Find the measure of the angle S. When the angle S is 45degree
Sol : Angle S +angle V= 90
45+angleV=90
Angle V= 90-45
Angle V= 45
Example problem related to vertical angles:
Q 1: Find the measures of angles when angle 1 is 45 when two straight lines intersect each other.
Sol :
Here the vertical opposite angles are equal.
So, angle 1= angle 2 (vertical opposite angles)
angle 3 = angle 4 (vertical opposite angles)
Angle1+angle 2 +angle 3+angle 4 = 360
45+45+ x+x =360
90 +2x=360
2x= 360-90
2x= 270
x= 270/2
x= 135
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Q 2 : Find the measures of angles when angle 1 is 55 when two straight lines intersect each other.
Sol :
Here the vertical opposite angles are equal.
So, angle 1= angle 2 (vertical opposite angles)
Angle 3 = angle 4 (vertical opposite angles)
Angle1+angle 2 +angle 3+angle 4 = 360
55+55+ x+x =360
110+2x=360
2x= 360-110
2x= 250
x= 250/2
x= 125
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