Question

Please solve this fast​

Answer 1

SoluTion:

Given:

• Angle PQR = 35°
• Angle QRP = 45°
• Angle BOP = 80°

To prove:

• P || m

Proof:

In ∆PQR, using angle sum property

→ 45° + 35° + Angle 1 = 180°

→ 80 + Angle 1 = 180°

→ Angle 1 = 180 - 80

→ Angle 1 = 100°

We know that,

• Verically opposite angles are equal.

Therefore, Angle 1 = Angle DPO

Hence, Angle DPO = 180°

We also know that,

• When sum of interior angles is of 180° then lines are parallel.

→ Angle BOP + Angle DPO should be of 180°

→ 80° + 100°

→ 180°

Thus, P || m

Hence Proved!

Answer 2

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$\color{blue}\large\underline{\underline{Answer:}}$

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In ∆PQR,

QRP + RPQ + PQR = 180° (Angle Sum Property)

45° + RPQ + 35° = 180°

RPQ + 80° = 180°

RPQ = 180° - 80°

RPQ = 100°

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RPQ + DPQ = 180° (Linear Pair)

100° + DPQ = 180°

DPQ = 180° - 100°

DPQ = 80°

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BOP = DPQ = 80°

i.e., Both the angles are corresponding to each other.

Hence, p // m.

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