1.

Consider the following parallelogram ABCD. Find the values of the unknown y and z.

Answer»

ong>Answer:

  • y = 50°
  • Z = 50°

Explanation:

Let the POINT of intersection of the two diagonals AC and BD = O

P.F.A the figure below for REFERENCE of angles

Given:

A PARALLELOGRAM ABCD in which:

  • ∠BCO = 40°
  • ∠CBO = y
  • ∠BOC = 90°
  • ∠ADO = z

To find:

  • The value of y and z

Proof:

In ΔBOC,

∠CBO + ∠BCO + ∠BOC = 180°                  (Angle Sum Property of Δ)

⇒ y + 40° + 90° = 180°

(Given, ∠BCO = 40°, ∠CBO = y, ∠BOC = 90°, ∠ADO = z)

⇒ y + 130° = 180°

⇒ y = 180° - 130°

⇒ y = 50°

Now, y = 50° = z            ( When AD || BC and BD is the transversal, Alternate

                                         interior angles are equal )

Hence,

  • y = 50°
  • z = 50°

Proved.

Hope you got that.

Thank you.



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