In the adjacent figure AB and CD at AB//CD, t is transversal intersecting E and F respectively. If angle 2:angle 1=5:4,find the measures of each marked angles
Answers
Given : AB || CD
t is transversal intersecting at E and F respectively.
∠2 : ∠1 = 5 : 4
To Find : measures of each angles
Solution:
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent.
• Alternate angles are congruent. ( Interiors & Exterior both )
• Interior angles are supplementary. ( adds up to 180°)
∠2 : ∠1 = 5 : 4
∠2 = 5K
∠1 = 4K
∠2 + ∠1 = 180° ( Linear pair)
5K + 4K = 180°
=> 9K = 180°
=> K = 20°
∠2 = 5K = 5* 20 = 100°
∠1 = 4K = 4* 20 = 80°
∠4 = ∠2 = 100° ( Vertically opposite angle)
∠3 = ∠1 = 80° ( Vertically opposite angle)
∠5 = ∠1 = 80° ( corresponding angles )
∠6 = ∠2 = 100° ( corresponding angles )
∠7 = ∠3 = 80° ( corresponding angles )
∠8 = ∠4 = 100° ( corresponding angles )
∠1 = 80°
∠2 = 100°
∠3 = 80°
∠4 = 100°
∠5 = 80°
∠6 = 100°
∠7 = 80°
∠8 = 100°
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