Question

6. In Fig. 8.92, which is the longer
(i) LM or MN, (ii) PQ or PR,
(iii) AB || DC; AB or BD?
(iv) PB or PC, given PB and PC bisect Zs ABC
and ZACB respectively.
(v) QM or QR if LM> LR and ZLMQ= ZLRQ.​

Answer 1

Solution :-

(i) in ∆LMN ,

→ ∠LMN + ∠LNM + ∠MLN = 180°

→ 58° + 63° + ∠MLN = 180°

→ 121° + ∠MLN = 180°

→ ∠MLN = 180° - 121°

→ ∠MLN = 59° .

since, sides opposite to greater angle is larger .

therefore,

→ 63° > 59° > 58°

→ ∠LNM > ∠MLN > ∠LMN

hence,

→ LM > MN > LN .

LM is longer than MN .

(ii) Must be given that, PQ || AR .

then,

→ ∠QPR = ∠PRS

→ ∠QPR = 80°

so,

→ ∠PQR = 42° { Exterior angle is equal to sum of opposite interior angles. }

also,

→ ∠PRQ = 180° - (80° + 42°)

→ ∠PRQ = 58°

then,

→ 58° > 42°

→ ∠PRQ > ∠PQR .

therefore,

→ PQ > PR .

hence, PQ is longer than PR .

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