In the adjoining figure, line p is parrall to line q and line m is parallel to line n, if angle 1 = 70° then find the measure of the angles angle 2, angle 3, angle 4, angle 5 and angle 6.
Answers
Given : line p is parallel to line q and line m is parallel to line n,
∠1 = 70°
To Find : ∠2 ,∠3 ,∠4 ,∠5 and ∠6
Solution :
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent.
• Alternate angles are congruent. ( Interiors & Exterior both )
• Co-Interior angles are supplementary. ( adds up to 180°)
Vertically opposite angles are equal
∠2 = ∠1 Vertically opposite angles
=> ∠2 = 70°
line p is parallel to line q and line m is parallel to line n,
Hence form a parallelogram
opposite angles of parallogram are equal
Hence ∠3 = ∠2
=> ∠3 = 70°
∠4 = ∠3 Vertically opposite angles
=> ∠4 = 70°
Corresponding angles of ∠1 makes linear pair with ∠5 and ∠6
∠1 + ∠5 = 180° and ∠1 + ∠6 = 180°
∠1 = 70°
=> ∠5 = ∠6 = 110°
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