Question

PQRS is a rhombus. If angle PRQ = 35°, what is the measure of angle PSQ

Answer 1

rhombus total measurement =90

angle PRQ=35

angle PSQ =90-35

angle PSQ=55 ans

hope it helps

Answer 2

Given:

Angle PRQ=35°

To find:

The angle PSQ

Solution:

The angle PSQ=55°.

In the rhombus PQRS, the angles formed at the adjacent vertices are supplementary.

So, angle QRS+ angle PSR=180° (1)

Also, the rhombus' diagonals bisect the angles QRS and PSR.

So, the angle PRQ=1/2 of angle QRS

Using values,

35°=1/2×angle QRS

35°×2=angle QRS

70°=angle QRS

Putting it in (1),

70°+angle PSR=180°

Angle PSR=180°-70°

Angle PSR=110°

Now, we have angle PSQ=1/2 of angle PSR

Using values,

Angle PSQ=1/2×110°

Angle PSQ=55°

Therefore, the angle PSQ=55°.