Question

7. In the given figure PQRS is a rectangle. Find the measure of x and y.
S
R
80°
0
To
Р
Q​

Answer 1

Answer:Let the point of intersection of the diagonals of the rectangle be O.

Given ∠OPQ=30°

∴∠SPO=60°  Similarly ∠RQO=60°

As its a rectangle, all the angles are 90°.

∴∠PQR=∠PQO+∠OQR

                 =30°+60°

                 =90°

∴∠OQR=60°    i.e, x=60°

From △POQ

Sum of angles of △les =180°

⇒∠OPQ+∠PQO+∠POQ=180°

∴∠POQ=180°−30

o

−30

o

=120°

i.e, ∠POQ=∠SOR=120°=y     [ i.e, opposite angles ]

∴ Sum of x+y=120°+60°=180°.

Hence, the answer is 180°.

Step-by-step explanation: