Question

the angel of a quadrilateral are in the ratio 3.4.5.6 find the angle​

Answer 1

Answer:

ratio=3:4:5:6

3x+4x +5x+6x =360

18x =360.

x=360/18 = 20.

3x = 3×20

= 60 .

4x= 4× 20

=80.

5x= 5×20

=100

6x= 6×20 .

120

Answer 2

Step-by-step explanation:

$\sf ratio \: given$

$\sf\bullet \: 3$

$\sf \bullet \: 4$

$\sf \bullet \: 5$

$\sf \bullet \: 6$

$\sf \: now \: lets \: take \: a \: common \: factor \: (x)$

$\sf \bullet\: 3 \times x = 3x \\ \\ \sf \bullet\:4 \times x = 4x \\ \\ \sf \bullet\:5 \times x = 5x \\ \\ \sf \bullet\:6 \times x = 6x$

$\sf \: We \: know \: that \: the \: total \: measure \: of \\ \sf \: any \: quadrilateral \: is \: 360$

$\sf \: We \: will \: add \: up \: all \: ratios$

$\sf \: 3x + 4x + 5x + 6x = 360 \\ \\ \sf \: 7x + 11x = 360 \\ \\ \sf \: 18x = 360 \\ \\ \sf \: x \: = \dfrac{360}{18} \\ \\ \sf x = 20$

$\sf \: Now \: we \: can \: find \: the \: angles \colon$

$\sf \: 3 \times 20 = 60 \degree \\ \\ \sf \: 4 \times 20 = 80 \degree \\ \\ \sf \: 5 \times 20 = 100 \degree \\ \\ \sf \: 6 \times 20 = 120 \degree$

$\sf \: We \: can \: verify \: it \: by \: adding \colon \\ \\ \sf \: 60 + 80 + 100 + 120 = 360 \degree \\ \\ \sf \: 140 + 220 = 360 \degree \\ \\ \sf \: 360 = 360 \degree \\ \\ \sf \: LHS = RHS$