7. In the given figure PQRS is a rectangle. Find the measure of x and y.
S
R
80°
0
To
Р
Q
Answers
Answered by
0
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:
Similar questions
English,
1 month ago
Math,
1 month ago
Business Studies,
1 month ago
Accountancy,
3 months ago
Geography,
9 months ago
Computer Science,
9 months ago