Question

the given figure pqrs is a rhombus in which diagonal PR is produced to T if angle is equal to 152 degree find X Y and Z

Answer 1

Angle srp=180-152°
Angle srp=28°

In rhombus, SR=SP

angle srp=z=28°. {By property of scalene triangle}

Y=90° { diagonals of rhombus bisects each other by 90°}

Angle spq=z=28°{ as diagonals of rhombus are angle bisector)


X+90°+28°=180°
X=180°-118
X=62°

Answer 2

Answer:

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.

$\angle SQP=\angle QSR=x$

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.