Question

In the adjoining figure, ABCD is a rhombus and ∠BCD =80
, find x, y, z, a.​

Answer 1

Answer:

might be it is helpful to you

Step-by-step explanation:

In rhombus ABCD, diagonals AC and BD bisect each other at 90°

∠BCD = 80°

Diagonals bisect the opposite angles also ∠BCD = ∠BAD (Opposite angles of rhombus)

∠BAD = 80° and ∠ABC = ∠ADC = 180° – 80° = 100°

Diagonals bisect opposite angles

∠OCB or ∠PCB = \frac { { 80 }^{ 0 } }{ 2 } = 40°

In ∆PCM,

Ext. CPD = ∠OCB + ∠PMC

110° = 40° + x

=> x = 110° – 40° = 70°

and ∠ADO = \frac { 1 }{ 2 } ∠ADC = \frac { 1 }{ 2 } x 100° = 50°

Hence x = 70° and y = 50°