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Solved Problems on Parallel linesIn 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 = 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). __________________________________________________________________ 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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