Question

5. In the parallelogram given alongside if angle Q = 110°, find all the other angles.
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Answer 1

In a Parallelogram,

i) Opposite Angles are Equal

ii) Adjacent Angles are Supplementary

Therefore, By Using i)

$∠S = 110°$

Now, By Using ii)

$∠P + ∠Q = 180 \\ ∠P + 110° = 180° \\ ∠P = 70°$

So, By Using i)

$∠R = 70°$

Answer 2

Solution :-

given that, PQRS is a parallelogram and ,

→ ∠Q = 110° .

Since PQRS is a parallelogram ,

→ PQ || SR { Opposite sides of parallelogram are parallel .}

→ RQ = A transversal .

So,

→ ∠Q + ∠R = 180° { Interior angles on the same side of the transversal are supplementry .}

→ 110° + ∠R = 180°

→ ∠R = 180° - 110°

→ ∠R = 70°

therefore,

→ ∠Q = ∠S = 110° { Opposite angles of ll gm are equal in measure . }

→ ∠P = ∠R = 70° { Opposite angles of ll gm are equal in measure . }

Hence,

→ ∠P = 70°

→ ∠R = 70°

→ ∠S = 110°

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