Question

PQRS is a rhombus, where
∠RQS = 47°. Find the following
angles: (i) ∠PSQ (ii) ∠SRQ (iii) ∠SPR

Answer 1

Given:

PQRS is a rhombus

∠RQS = 47°

To find:

(i) ∠PSQ

(ii) ∠SRQ

(iii) ∠SPR

Answer:

i)

Since PQRS is a rhombus.

∠RQS= ∠PSQ = 47°(alternate int. Angle)

Now, we know that the diagonals bisects the interior angle.

So, ∠PSR=2∠PSQ= 2x47°= 94

And ∠PSQ=∠QSR=47°

ii)

Now,see the Rhombus...SRQis a triangle...

Sum of all sides of a triangle= 180°

= ∠RQS+∠SRQ+∠QSR=180°

=47+47+∠QRS=180

∠SRQ= 180-94= 86

iii)

∠SPR=∠QRP (alternate interior angle)

∠QRP=Half of ∠SRQ= 86/2= 43

So, ∠SPR=43°