Question

Find the angles A B C and D

Answer 1

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

Answer 2

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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