In the following figure RISK and CLUE are parallelograms. Find the

1.	In the following figure RISK and CLUE are parallelograms. Find the measure of x.
Answer» In parallelogram RISK ∠RKS + ∠KSI = 180° [sum of the adjacent angles is equal to 180° in a parallelogram] 120° + ∠KSI = 180° ∠KSI = 180° – 120° ∠z = 60° In parallelogram CLUE ∠CEU = ∠z = 70° [opposite angles are equal in a parallelogram] In ΔEOS 70° + ∠x + 60° = 180° [Sum of angles of a triangles is 180°] ∠x = 180° – 130° ∠x = 50° ∴ x = 50°

In the following figure RISK and CLUE are parallelograms. Find the measure of x.

Answer»

In parallelogram RISK

∠RKS + ∠KSI = 180° [sum of the adjacent angles is equal to 180° in a parallelogram]

120° + ∠KSI = 180°

∠KSI = 180° – 120°

∠z = 60°

In parallelogram CLUE

∠CEU = ∠z = 70° [opposite angles are equal in a parallelogram]

In ΔEOS

70° + ∠x + 60° = 180° [Sum of angles of a triangles is 180°]

∠x = 180° – 130°

∠x = 50°

∴ x = 50°