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

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