Question

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

Answer 1

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.