Question

In the figure, PQRS is a rhombus and SRB = 68º. Find x, y and z.​

Answer 1

Step-by-step explanation:

X = Y=Z= 64

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Answer 2

Answer:

x = 66°, y = 56°, and z = 56°

Step-by-step explanation:

Given:- PQRS is a rhombus and ∠SRB = 68°

To find:- x, y and z

Proof:-

We know that,

In a Rhombus,

• Diagonals bisect the angles
• Opposite angles are equal
• Adjoining angles are supplementary

Now,

∠SRB = 68°

Also,

∠SRB + ∠RSP = 180°

68° + ∠RSP = 180°

∠RSP = 180° - 68°

∠RSP = 112° ----- 1

We also know that,

∠RSO = ∠PSO = y ------ 2

Now,

∠RSP = ∠RSO + ∠PSO

From eq.2,

∠RSP = ∠RSO + ∠RSO

∠RSP = 2∠RSO

From eq.1 and eq.2,

112° = 2y

y = 112/2

y = 56°

We also know that,

∠RSP = ∠RQP

Hence,

∠RQP = 112° ----- 3

And

∠RQS = ∠PQS = z ------ 4

But,

∠RQP = ∠RQS + ∠PQS

From eq.4

∠RQP = ∠PQS + ∠PQS

∠RQP = 2∠PQS

From eq.3 and eq.4,

112° = 2z

z = 112/2

z = 56°

Now, similarly

2∠ARB = ∠SRB

∠ARB = 68°/2

∠ARB = 34° ----- 5

Also,

OR is a straight line,

Thus,

∠OAB + ∠BAR = 180° [Linear Pair]

100° + ∠BAR = 180°

∠BAR = 180° - 100°

∠BAR = 80° ----- 6

In ΔBAR,

∠BAR + ∠RBA + ∠ARB = 180° [Angle Sum Property]

From eq.5 and eq.6,

80° + x + 34° = 180°

x + 114° = 180°

x = 180° - 114°

x = 66°

Hence,

x = 66°, y = 56°, and z = 56°

Hope it helped and believing you understood it........All the best