Question

Points A, B, C and D are on the circle. The ∠ACB and ∠ADB are angles subtended by the same arc AB. If arc AB measures (5x – 30)° and m∠ACB = (x + 15) °, what is m∠ADB?

Answer 1

Given :- Points A, B, C and D are on the circle. The ∠ACB and ∠ADB are angles subtended by the same arc AB. If arc AB measures (5x – 30)° and m∠ACB = (x + 15)° .

To Find :- m∠ADB = ?

Answer :-

from image , let O is the centre of the circle .

so,

→ ∠AOB = Length of arc AB { Measure of an arc is the measure of its corresponding central angle. }

→ ∠AOB = (5x - 30)°

then,

→ ∠ACB = (1/2)∠AOB { Angle at circumference is half of angle at centre by same chord. }

→ (x + 15)° = (1/2)(5x - 30)°

→ 2x + 30° = 5x - 30°

→ 30° + 30° = 5x - 2x

→ 3x = 60°

→ x = 20° .

therefore,

→ ∠ADB = ∠ACB { Angle formed by same chord on circumference are equal.}

→ ∠ADB = (x + 15)°

→ ∠ADB = (20 + 15)°

→ ∠ADB = 35° (Ans.)

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