Question

21. In the given figure below, P = 40°, PQR = 60°. If <PQR = 60°. If OQ
and OR are the bisectors of the angles PQR and PRQ respectively. Find the
angles angle ORQ and <QOR.
​

Answer 1

Answer:

Correct Question:

In the figure angle p = 60 If QO,RO are bisectors of angle Q and angle R respectively . Find the of angle QOR.

GIVEN:

$\sf∠P = 60° \\ </p><p></p><p> \sf∠OQP = ∠OQR \\ \sf [ QO , \: OR \: are \: </p><p></p><p> the \: bisectors \: of \: ∠Q and ∠R] \\ \sf ∠PRO = ∠ORQ$

TO FIND:

$\sf \: \pink{ ∠QOR}$

SOLUTION:

$\sf \: In ΔPQR \\ </p><p></p><p>\sf \:∠OQP = ∠OQR = x \\ </p><p></p><p>\sf \:∴∠PQR = ∠PQO + ∠OQR = x+x =2x \\ </p><p></p><p>\sf \:∠PRO = ∠ORQ = x \\ </p><p></p><p>\sf \:∴∠PRQ = ∠PRO + ∠ORQ = x+x = 2x \\ </p><p></p><p>\sf \:∠PQR +∠PRQ + ∠QPR = 180° [ SUM \: OF Δ] \\ </p><p></p><p>\sf \:2x+2x + 60° = 180° \\ </p><p></p><p>\sf \:4x = 180°- 60° = 120°$

$\sf \: x = \frac{120}{4} = 30 {}^{o}$

$\sf∠PRO = 30°</p><p></p><p>\sf∠ORQ = 30° \\ </p><p></p><p>\sf∠PQO = 30° \\ </p><p></p><p>\sf∠OQR = 30° \\ </p><p></p><p>\sf∠PRQ = x+x = 60° \\ </p><p></p><p>\sf∠PQR = x+x = 60° \\ </p><p></p><p>\sf \: In Δ OQR \\ </p><p></p><p>\sf∠PQO +∠OQR +∠QOR = 180° \\ \sf[ SUM \: OF Δ] \\ </p><p></p><p>\sf30° +30° +∠QOR = 180°</p><p>$

$\sf \pink{∠QOR = 180° - 60° = 120°}$