Solved Problems on Parallel lines

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

Examples :

1) In the given figure line l is parallel to line m. ∠ c = 110⁰. Find the measures of remaining angles.

Solution :
∠ c = 110⁰

∠ c = ∠ g ( Corresponding angles)

∴ ∠g = 110⁰

∠ c = ∠ e ( Alternate interior angles)
∠ e = 110⁰

∠ e = ∠ a (Corresponding angles)

∠ a = 110⁰

∠ 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 = 70⁰

∠ 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).
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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

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