Question

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

Answer 1

$\Large{\underbrace{\sf{\purple{Required\:Answer:}}}}$

⛦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°.

Answer 2

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 = ($\frac{280}{7}$)  °

⇒ 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.