Alright, lets get started.
If two angles have common side and they shares common vertex, they are called adjacent angles.
When two lines crosses each other, the opposite angles are called vertical angles as they share same vertex.
Question 4:
Two angles shown in diagram are adjacent as they are on common side.
Both the angles are on a straight line, hence
[tex] x + 109 = 180 [/tex]
Subtracting 109 from both sides
[tex] x + 109 - 109 = 180 - 109 [/tex]
[tex] x = 71 [/tex]° : Answer
Question 5:
Both angles shown in diagram are opposite to each other, hence vertical angles.
As they are opposite to each other, they both are equal.
[tex] x+42= 2x + 1 [/tex]
Subtracting x from both sides
[tex] x + 42 - x = 2x + 1 - x [/tex]
[tex] 42 = x + 1 [/tex]
Subtracting 1 from both sides
[tex] 42 - 1 = x + 1 - 1 [/tex]
[tex] x = 41 [/tex]° : Answer
Question 6:
Both angles are having a common side means they are adjacent angles.
As they are on straight line, both angles will add up to 180 °.
[tex] x+96 + 5x = 180 [/tex]
[tex] 6 x + 96 = 180 [/tex]
Subtracting 96 from both sides
[tex] 6x + 96 - 96 = 180 - 96 [/tex]
[tex] 6x= 84 [/tex]
Dividing from 6 in both sides
[tex] \frac{6x}{6} =\frac{84}{6} [/tex]
[tex] x = 14 [/tex]° : Answer
Hope it will help :)
