Question

In the given figure, PQRS is a rhombus, such that PRQ = 45º then, find the measure of
PSQ

Answer 1

Given:

In the given figure, PQRS is a rhombus, such that PRQ = 45º

To Find:

find the measure of  PSQ

Solution:

In the given figure we can see it is a rhombus, where we know that PQ is parallel to SR and PS is parallel to QR, the intersection of diagonal is point O and the diagonals of a rhombus intersect at 90 degrees.

Now if PRQ is 45 degrees then angle RPS will also be 45 degrees as PS and QR are parallel to each other and PR is a transversal line, so now in a triangle POS, we have,

$\angle OPS=45^{\circ}\\\angle PSO=\theta\\\angle POS=90^{\circ}$

now using the property of triangle that the sum of all the interior angles is equal to 180 degrees, so we have,

$\angle POS+\angle OSP+\angle SPO=180^{\circ}\\90+\theta +45=180\\\theta=180-90-45\\\theta=45^{\circ}$

Hence, the value of angle PSQ is 45 degrees.