Question

the ratio between the three quadrilateral is 3 : 5 : 9, the value of the fourth angle of the quadrilateral is 71 degree. what is the difference between the largest and the smallest angle of the quadrilateral​

Answer 1

Answer:

Let the common multiple be x

The four angles of quadrilateral be 3x, 5x, 9x, 71

Sum of all angles of quadrilateral is 360°

Hence,

3x + 5x + 9x + 71 = 360

17x = 360 - 71

17x = 289

x = 17

The angles of quadrilateral are:

3x = 3 × 17 = 51

5x = 5 × 17 = 105

9x = 9 × 17 = 153

Largest angle = 153°

Smallest angle = 51°

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Answer 2

102°

Step-by-step explanation:

Let us assume that in aquadrilateral ABCD the three angles of a quadrilateral are 3x,5x,9x,and Fourth angle is 71°.

We know that,Sum of angles of a quadrilateral is 360°.

⇒∠A+∠B+∠C+∠D=360°

⇒3x+5x+9x+71°=360°

⇒ 17x+71°=360°

⇒17x=360°-71°

⇒17x=289°

⇒x=17°

So that,∠$A=3\times 17=51$°

∠$B=5\times 17=85$°

∠$C=9\times 17=153$°

Now,we have to find

∠C-∠D=153°-51°

           =102°