Question

In Fig. 14.113, PQRS is a rhombus in which the diagonal PR is produced to T. If ∠SRT=152°, find x,y and z.

Answer 1

Given : PQRS is a rhombus in which the diagonal PR is produced to T and ∠SRT = 152°.

 

We know that diagonals of a rhombus bisects each other at right angle i,e 90°.

Hence , ∠SOR = 90° = y = 90°

∠SRT + ∠SRO = 180° (Linear pair)

= 152°+ ∠SRO = 180°

∠SRO = 180° - 152°

∠SRO  = 28°

 

Now, SR = SP  

[sides of a rhombus are equal]

∠SRO = z  

[Angle opposite to equal sides are equal ]

z  = ∠SRO  = 28°

 

In SOR ,  

We know that sum of all angles of a triangle is 180°.

∠RSO + ∠SRO + y = 180°

= ∠RSO + 28° + 90° = 180°

= ∠RSO + 118° = 180°

= ∠RSO = 180°- 118°  

∠RSO = 62°

∠X = ∠RSO = 62° (alternate angles)

Hence, the values of x is  62° , y is 90° and z is  28°.

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

The value of x, y and z are 62, 90 and 28 respectively.

Step-by-step explanation:

Given information: PQRS is a rhombus, ∠SRT =152°.

The diagonals of thrombus are perpendicular bisector of each other.

The angle y is included angle of both diagonals, therefore

$\angle y=90^{\circ}.$

The inclined angles of isosceles triangle are equal.

Triangle PRS is an isosceles triangle because PS=RS.

$\angle SPR=\angle SRP = z$

180-152=z

$28^{\circ}=z \:$

Angle SQP and angle QSR are alternate interior angle.

∠SQP=∠QSR=x

Using exterior angle theorem,

x+y=152

x+90=152

$x=62^{\circ} \:$

Therefore the value of x, y and z are 62, 90 and 28 respectively.