The diagonals PR and QS of a parallelogram PQRS intersect each other at ‘O’. If ∠SPR=30°and ∠POQ= 72° then ∠SQR is equal to-
Answers
∠SQR = 42°
Step-by-step explanation:
GIVEN
- ∠SPR=30°
- ∠POQ= 72°
___________________________
TO FIND
- ∠SQR
___________________________
We know that,
- Sum of linear pair is 180°
- ∠POQ + ∠POS = 180° [ Linear Pair ]
- 72° + ∠POS = 180°
- ∠POS = 180° - 72°
- ∠POS = 108°
∠POS = 108°
___________________________
We know that,
- Sum of all interior angels of a triangle is 180°
Here,
- POS is triangle
- ∠POS + ∠SPR + ∠PSO = 180° [ Interior Angles ]
- 108° + 30° + ∠PSO = 180°
- 138° + ∠PSO = 180°
- ∠PSO = 180° - 138°
- ∠PSO = 42°
∠PSO = 42°
___________________________
We know that,
- Interior angles of a parallelogram which is interested by a diagonal are equa
Here,
- ∠PSO = ∠SQR [ Interior Angles Of A Parallelogram Intersected By Diagonal ]
- ∠PSO = 42°
- ∠SQR = 42°
∠SQR = 42°
→ ANSWER :
∠SPR=30°
∠POQ= 72°
___________________________
TO FIND
∠SQR
___________________________
We know that,
Sum of linear pair is 180°
∠POQ + ∠POS = 180° [ Linear Pair ]
72° + ∠POS = 180°
∠POS = 180° - 72°
∠POS = 108°
∠POS = 108°
___________________________
We know that,
Sum of all interior angels of a triangle is 180°
Here,
POS is triangle
∠POS + ∠SPR + ∠PSO = 180° [ Interior Angles ]
108° + 30° + ∠PSO = 180°
138° + ∠PSO = 180°
∠PSO = 180° - 138°
∠PSO = 42°
∠PSO = 42°
___________________________
We know that,
Interior angles of a parallelogram which is interested by a diagonal are equa
Here,
∠PSO = ∠SQR [ Interior Angles Of A Parallelogram Intersected By Diagonal ]
∠PSO = 42°
∠SQR = 42°
∠SQR = 42°
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