Question

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Answer 1

Given:

• Two lines AB and CD are parallel.
• AB intersects PQ at N and QR at O.
• CD intersects PQ at M and QR at L.

To Find:

• The value of ∠PQR .

Answer:

Some points to be remembered here,

• Alternate interior angles are equal.
• Corresponding angles are equal.
• Sum of co - interior angles is 180°.

Now , ∠ PNO and ∠NML are alternate interior angles. So they will be equal ,

Hence ∠PNO = ∠ NML = 88°.

Also , ∠NML + ∠ LMQ = 180° (linear pair)

⟹ 88° + ∠LMQ = 180°.

⟹ ∠LMQ = 180°-88°.

.°. ∠ LMQ = 92°.

Similarly , ∠OLM and ∠QLM are angles in straight line ,

⟹ ∠OLM + ∠QLM = 180°.

⟹ 110° + ∠QLM = 180° .

⟹ ∠QLM = 180° - 110°.

.°. ∠ QLM = 70°.

$\rule{200}4$

Now , in ∆QLM ,

⟹ ∠QLM + ∠LMQ + ∠LQM = 180°.

⟹ 70°+ 88° + ∠LQM = 180°.

⟹ 162° + ∠PQR = 180°.

⟹ ∠PQR = (180-162)°.

.°. ∠PQR = 18° .

Hence the value of ∠PQR is 18° .

Answer 2

Answer:

Step-by-step explanation:

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