# Solved Problems on Intersecting Lines

Here we will discuss some solved problems on intersecting lines.

Intersecting lines include vertically opposite angels, linear pair angles,adjacent angles etc.

Some solved problems on intersecting lines

Q.1 Find the value of x in each of the following figures.
A) Solution :
We have,
75 + 47 + x + 83 + 92 = 3600
297 + x = 3600
∴ x = 360 – 297
⇒ x = 630

_________________________________________________________________
B) Solution
POS is a straight line ⇒ ∠POS = 1800
60 + 4x + 40 = 180 sup>0
100 + 4x = 180
4x = 180 – 100
4x = 80
x = 80/4
x = 20.
_________________________________________________________________
C) Solution:
According to the given figure, sum of all the angles is equal to 3600
2x + x + 2x + 3x = 3600
8x = 360
x = 360/8
x = 45
_________________________________________________________________
D) Find the value of the angles x, y and z in each of the following figures: (i) x and 55° are vertically opposite angles,
so, x = 55°and y are linear pair,
∴ y + 55° = 180°
⇒ y= 125°
y and z are vertically opposite angles.
∴ y= z
⇒ y = z = 125
Hence,x= 55° and y= z = 125°
(ii) 40, x and 25 are linear pair
∴ 40+ x + 25= 180
⇒ x = 180- 40- 25
⇒ x = 115
40 and y are linear pair
40+ y = 180
y = 180- 40
= 140
Now, y and z are linear pair
∴ y + z = 180
140+ z = 180
z = 180- 140
z = 40
Hence, x = 1150, y = 1400, z = 400

Basic Geometry

Point
Lines
Angles
Lines and Angles
Complementary angles
Supplementary angles
Vertically Opposite Angles
Linear Pair Angles