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

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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.
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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
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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
• Adjacent Angles
• Parallel Lines
• Solved Problems on Intersecting Lines
• Solved Problems on Parallel Lines

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