In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is: 1. 30° 2. 60° 3. 90° 4. 120°

From figure, ∠ACD and ∠ACB forms linear pairs [BD is a straight line]. ⇒ ∠ACD + ∠ACB = 180° ⇒ 120° + ∠ACB = 180° ⇒ ∠ACB = 180° - 120° ⇒ ∠ACB = 60°. In ΔABC, ⇒ BC = AC [Given] ⇒ ∠ABC = ∠BAC = x° (let) [Angles opposite to equal sides in triangle are equal] According to angle sum property in ΔABC, ⇒ ∠ACB + ∠ABC + ∠BAC = 180° ⇒ 60° + x° + x° = 180° ⇒ 2x° = 180° - 60° ⇒ 2x° = 120° ⇒ x° = = 60°. From figure, ABCE is cyclic quadrilateral. We know that, Opposite angles of cyclic quadrilateral are supplementary. ⇒ ∠ABC + ∠AEC = 180° ⇒ 60° + ∠AEC = 180° ⇒ ∠AEC = 180° - 60° ⇒ ∠AEC = 120°. Hence, option 4 is the correct option.

The equation of the line passing through origin and parallel to the line 3x + 4y + 7 = 0 is:
3x + 4y + 5 = 0
4x - 3y - 5 = 0
4x - 3y = 0
3x + 4y = 0

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The factor common to the two polynomials x² - 4 and x³ - x² - 4x + 4
(x + 1)
(x - 1)
(x - 2)
(x - 4)

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A man invested in a company paying 12% dividend on its share. If the percentage return on his investment is 10%, then the shares are:
at par
below par
above par
cannot be determined

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Mathematics

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is:
30°
60°
90°
120°

Circles

Related Questions

The equation of the line passing through origin and parallel to the line 3x + 4y + 7 = 0 is:
3x + 4y + 5 = 0
4x - 3y - 5 = 0
4x - 3y = 0
3x + 4y = 0

The factor common to the two polynomials x² - 4 and x³ - x² - 4x + 4
(x + 1)
(x - 1)
(x - 2)
(x - 4)

A man invested in a company paying 12% dividend on its share. If the percentage return on his investment is 10%, then the shares are:
at par
below par
above par
cannot be determined

Mathematics

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is:30°60°90°120°

Circles

Related Questions

The equation of the line passing through origin and parallel to the line 3x + 4y + 7 = 0 is:3x + 4y + 5 = 04x - 3y - 5 = 04x - 3y = 03x + 4y = 0

The factor common to the two polynomials x2 - 4 and x3 - x2 - 4x + 4(x + 1)(x - 1)(x - 2)(x - 4)

A man invested in a company paying 12% dividend on its share. If the percentage return on his investment is 10%, then the shares are:at parbelow parabove parcannot be determined

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is:
30°
60°
90°
120°

The equation of the line passing through origin and parallel to the line 3x + 4y + 7 = 0 is:
3x + 4y + 5 = 0
4x - 3y - 5 = 0
4x - 3y = 0
3x + 4y = 0

The factor common to the two polynomials x² - 4 and x³ - x² - 4x + 4
(x + 1)
(x - 1)
(x - 2)
(x - 4)

A man invested in a company paying 12% dividend on its share. If the percentage return on his investment is 10%, then the shares are:
at par
below par
above par
cannot be determined