# Solved Problems on Parallel lines

In this section, we will discuss some solved problems on parallel lines.

1) In the given figure line l is parallel to line m. ∠ c = 110

∠ c = 110

∠ c = ∠ g ( Corresponding angles)

∴ ∠g = 110

∠ c = ∠ e ( Alternate interior angles)

∠ e = 110

∠ e = ∠ a (Corresponding angles)

∠ a = 110

∠ a and ∠ b form a linear pair angles. And linear pair angles are supplementary .( two angles add up to 180)

∴ ∠ a + ∠ b = 180

110 + ∠ b = 180

∠ b = 180 -110

∠ b = 70

∠ b = ∠ f (Corresponding angles)

∠ f = 70

∠ f = ∠ d ( Alternate interior angles)

∠ d = 70

∠ d = ∠ h ( Corresponding angles)

∴ ∠ h = 70

2) State which of the lines are parallel and why?

a)

AC || DE ( As alternate interior angles are equal)

b)

__________________________________________________________________

1) Define Adjacent angles.

2) Two acute angles form linear pair angles.(True/False)

3)Which shape relevant to alternate interior angles. a)

b)

4) If the corresponding angles are equal then what can you say about the lines.

5) If ∠A = 2x and ∠B=3x and the two angles are interior angles on the same side of the transversal then find the value of x and measures of each angle.

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**Examples :**1) In the given figure line l is parallel to line m. ∠ c = 110

^{0}. Find the measures of remaining angles.**Solution :**∠ c = 110

^{0}∠ c = ∠ g ( Corresponding angles)

∴ ∠g = 110

^{0}∠ c = ∠ e ( Alternate interior angles)

∠ e = 110

^{0}∠ e = ∠ a (Corresponding angles)

∠ a = 110

^{0}∠ a and ∠ b form a linear pair angles. And linear pair angles are supplementary .( two angles add up to 180)

∴ ∠ a + ∠ b = 180

110 + ∠ b = 180

∠ b = 180 -110

∠ b = 70

^{0}∠ b = ∠ f (Corresponding angles)

∠ f = 70

^{0}∠ f = ∠ d ( Alternate interior angles)

∠ d = 70

∠ d = ∠ h ( Corresponding angles)

∴ ∠ h = 70

2) State which of the lines are parallel and why?

a)

**Solution :**AC || DE ( As alternate interior angles are equal)

b)

**Solution:**AC is not parallel to DE ( As corresponding angles are not equal).__________________________________________________________________

**Practice**

1) Define Adjacent angles.

2) Two acute angles form linear pair angles.(True/False)

3)Which shape relevant to alternate interior angles. a)

**F**b)

**Z**4) If the corresponding angles are equal then what can you say about the lines.

5) If ∠A = 2x and ∠B=3x and the two angles are interior angles on the same side of the transversal then find the value of x and measures of each angle.

**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