Question

7. Three angles of a quadrilateral are in the ratio 2:3:7. The mean of these angles is 64°
Find the fourth angle.
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Answer 1

SOLUTION:

Let the three angles be 2x,3x &7x

Mean of angles;

$= > \frac{Sum \: of \: angles}{number \: of \: angles}$

$= > \frac{2x + 3x + 7x}{3} \\ \\ = > \frac{12x}{3} \\ \\ = > 4x$

But, mean = 64 [given]

=) 4x= 64

=) x= 64/4

=) x= 16°

So,

1st angle, 2x = 2×16°= 32°

2nd angle, 3x= 3× 16°= 48°

3rd angle, 7x= 7 × 16°= 112°

Now, we know that the sum of all quadrilateral sides= 360°

Let the fourth angle be y.

A/q

=) 32°+ 48°+ 112°+ y°= 360°

=) 192° + y°= 360°

=) y°= 360° -192°

=) y = 168°

Fourth angle= 168°

Hope it helps ☺️

Answer 2

Answer:

Fourth angle of quadrilateral is 168 .

Step-by-step explanation:

Let the unit constant be k

Given ;

Three ratio and it mean

2 k + 3 k + 7 k = 64 × 3

12 k = 64 × 3

k = 16

Three three angle are as ;

32 , 48 and 112 respectively.

We have to find fourth angle of quadrilateral.

Let fourth angle be a

Now sum of interior quadrilateral is 360

23 + 48 + 112 + a = 360

a = 360 - 192

a = 168

Thus the fourth angle of quadrilateral is 168 .