19) In a quadrilateral three angles are in the ratio 3 : 3:1 & one of the
angle is 80″,then find the other angles.​

19) In a quadrilateral three angles are in the ratio 3 : 3:1 & one of the
angle is 80″,then find the other angles.​

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2 thoughts on “<br />19) In a quadrilateral three angles are in the ratio 3 : 3:1 & one of the<br />angle is 80″,then find the other angles.​”

  1. Answer:

    1. ∠ A = 120 °
    2. ∠ B = 120 °
    3. ∠ C = 40 °
    4. ∠ D = 80 °

    Explanation:

    Given:

    • A quadrilateral in which:
    1. Ratio of three angles = 3 : 3 : 1
    2. Measure of 4th angle = 80 °

    To find:

    The measure of the other three angles.

    Proof:

    P.F.A the figure below for reference.

    Let the given quadrilateral be ABCD.

    According to the question, Let:

    1. ∠ A = 3x
    2. ∠ B = 3x
    3. ∠ C = x
    4. ∠ D = 80 °

    Now,

    ∠ A + ∠ B + ∠ C + ∠ D = 360 °

    [ Sum of the interior angles of a quadrilateral = 360 ° ]

    Substituting the values of ∠A, ∠B, ∠C, & ∠D, we get:

    = 3x + 3x + x + 80 ° = 360 °

    ⇒ 7x + 80 ° = 360 °

    ⇒ 7x = (360 – 80) °

    ⇒ 7x = 280 °

    ⇒ x = ([tex]\frac{280}{7}[/tex]) °

    ⇒ x = 40 °

    Substituting the value of x in ∠A, ∠B, ∠C we get:

    1. ∠ A = 3(40) = 120 °
    2. ∠ B = 3(40) = 120 °
    3. ∠ C = x = 40 °

    Hence,

    1. ∠ A = 120 °
    2. ∠ B = 120 °
    3. ∠ C = 40 °
    4. ∠ D = 80 ° [Given]

    Proved.

    Hope you got that.,

    Thank You.

    Reply
  2. [tex]\Large{\underbrace{\sf{\purple{Required\:Answer:}}}}[/tex]

    ⛦Given,

    ratio is 3:3:1 and fourth angle is 80°.

    Sum of all the angles of the quadrilateral is 360°.

    Let the ratio numbers be:

    ⟼3x, 3x and 1x

    ⟼3x + 3x + 1x + 80° = 360°

    ⟼7x + 80° = 360°

    ⟼7x = 360° – 80°

    ⟼7x = 280°

    3x = 3 / 7 x 280°

    = 3 x 40

    = 120°

    3x = 3 / 7 x 280°

    = 3 x 40

    = 120°

    1x = 1 / 7 x 280°

    = 1 x 40

    = 40°

    • ↬Therefore, the four angles are 120°, 120°, 40° and 80°.
    Reply

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