# Ex 3.3, 2 - Chapter 3 Class 8 Understanding Quadrilaterals

Last updated at Aug. 4, 2018 by Teachoo

Last updated at Aug. 4, 2018 by Teachoo

Transcript

Ex 3.3, 2Consider the following parallelograms. Find the values of the unknowns x, y, z.(1)Given, a Parallelogram ABCD where ∠B = 100° We know that, Adjacent angles of a Parallelogram are supplementary. ∠ A + ∠B = 180° z + 100° = 180° z + 100° = 180° z = 180° − 100° z = 80° Also, In parallelogram, opposite angles are equal Therefore, x = 80° , y = 100° and z = 80° Ex 3.3, 2Consider the following parallelograms. Find the values of the unknowns x, y, z.(ii) Let the parallelogram be ABCD In parallelogram, Adjacent angles are Supplementary ∠A + ∠D = 180° x + 50° = 180° x = 180° − 50° x = 130° ∠C + ∠D = 180° y + 50° = 180° y = 180° − 50° y = 130° Also, Opposite angles of a Parallelogram are equal ∠ABC = ∠ D ∠ ABC = 50° Now, ABO is a line So, by linear pair ∠ ABC + z = 180° 50° + z = 180° z = 180° − 50° z = 130° Therefore, x = 130° , y = 130° and z = 130° Ex 3.3, 2Consider the following parallelograms. Find the values of the unknowns x, y, z.(iii)Let the Parallelogram be ABCD where ∠BCO = 30° and ∠AOD = 90° Now, AC and BD intersect each other at O x = 90° In ∆BOC, Sum of all angles = 180° y + x + 30° = 180° y + 90° + 30° = 180° y + 120° = 180° y = 180° − 120° y = 60° Now, ABCD is a parallelogram ∴ AD ∥ BC and BD is a transversal , ∠ODA = ∠OBC z = y z = 60° Therefore, x = 90°, y = 60° and z = 60° Ex 3.3, 2Consider the following parallelograms. Find the values of the unknowns x, y, z. Let the parallelogram be ABCD where ∠ B = 80° We know that, Sum of Adjacent angles of a Parallelogram is 180° ∠A + ∠B = 180° x + 80° = 180° x = 180° − 80° x = 100° Also, Opposite angles of parallelogram are equal ∠B = ∠D y = 80° ∠BCD = ∠A ∠ BCD = x = 100°Now, BCO is a line ∠BCD + ∠ OCD = 180° 100° + z = 180° z = 180° − 100° z = 80° Therefore, x = 100° , y = 80° and z = 80°

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.