Find the angles A B C and D
Answers
Step-by-step explanation:
<c = 83 [Vertically Opposite angle]
<a = 180 - 79 [linear pair]
= 101
<b = 180 - <a [Its a trapezium (Sum Adjacent angle is 180 expect <d)]
= 79
<d = 180 - <c [Its a trapezium (Sum Adjacent angle is 180 expect <b)]
= 97
Given : A Quadrilateral with one pair of lines parallel
To Find : Angles a , b , c and d
Solution:
"Linear pair of angles adds up to 180°"
angle a and 79° forms a linear pair.
Hence a + 79° = 180°
=> a = 101°
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent. ( Equal in Measure)
• Alternate angles are congruent. ( Interiors & Exterior both )
• Co-Interior angles are supplementary. ( adds up to 180°)
∠b = 79° ( corresponding angles)
∠c = 83° ( vertically opposite angles are equal )
∠c + ∠d = 180° ( Co-Interior angles )
Substitute ∠c = 83°
83° + ∠d = 180°
∠d = 97°
Measure of a , b , c and d are 101° , 79° , 83° and 97° respectively.
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