Question
In the given parallelogram YOUR, ∠RUO=120∘ and OY is extended to point S, such that ∠SRY=50∘. Find ∠YSR.
In the given parallelogram YOUR, ∠RUO=120∘ and OY is extended to point S, such that ∠SRY=50∘. Find ∠YSR.
Answer:
:
Given, ∠RUO=120∘ and ∠SRY=50∘
∠RYO=∠RUO=120∘ [∵ opposite angles of a parallelogram]
Now, ∠SYR=180∘−∠RYO [linear pair]
=180∘−120∘=60∘
In ΔSRY,
By the angle sum property of a triangle, ∠SRY+∠RYS+∠YSR=180∘
⇒50∘+60∘+∠YSR=180∘⇒∠YSR=180∘−(50∘+60∘)=70∘.
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:
Given, ∠RUO=120∘ and ∠SRY=50∘
∠RYO=∠RUO=120∘ [∵ opposite angles of a parallelogram]
Now, ∠SYR=180∘−∠RYO [linear pair]
=180∘−120∘=60∘
In ΔSRY,
By the angle sum property of a triangle, ∠SRY+∠RYS+∠YSR=180∘
⇒50∘+60∘+∠YSR=180∘⇒∠YSR=180∘−(50∘+60∘)=70∘.
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