Question

if 0 is the centre of the circle find the value of x​

Answer 1

ᴀɴsᴡᴇʀ

we have,

• ∠POQ = 60° (on centre O of a circle)

here,

∠POR + ∠RPQ = 180°

( linear pair : sum of angles of a straight line is 180°)

➪ 60° + ∠ROQ = 180°

➪ ∠ROQ = 180° - 60°

➪ ∠ROQ = 120° .......(i)

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and ∠PRQ = 1/2 ∠POQ

★ by theorem : Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.

➪ ∠PRQ = 1/2 × 60°

➪ ∠PRQ = 30° .......(ii)

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now, in ∆ROQ

∠R + ∠O + ∠Q = 180°

★ by theorem : sum of all interior angles of a triangle is 180°

➪ ∠PRQ + ∠ROQ + ∠RQO = 180°

and we have,

• ∠ROQ = 120° ......(i)
• ∠ROQ = 30° .......(ii)

➪ 120° + 30° + x = 180°

➪ 150° + x = 180°

➪ x = 180° - 150°

➪ x = 30°

therefore, value of x is 30°