# 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 = 360

^{0}

297 + x = 360

^{0}

∴ x = 360 – 297

⇒ x = 63

^{0}

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B)

**Solution**

POS is a straight line ⇒ ∠POS = 180

^{0}

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 360

^{0}

2x + x + 2x + 3x = 360

^{0}

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 = 115

^{0}, y = 140

^{0}, z = 40

^{0}

**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

• 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