Question

1. The angles A, B, C and D of a quadrilateral have
measures in the ratio 2:4:5:7. Find the measures
of these angles. What type of quadrilateral is it?
[CBSE 2012]
Give reasons.​

Answer 1

Answer:

$let \: 2 = 2x \\ 4 = 4x \\ 5 = 5x \\ 7 = 7x \\ add \: all \: the\: sides \:of \:quadilateral \: and \\ \:measure \: of \: all \: the \: sides \: are \: 360 \\ 2x + 4x + 5x + 7x = 360 \\18x = 360 \\x = 360 \div 18 \\ x = 20 \\ now \: 2x = 2 \times 20 =40 \\ 4x = 4 \times 20 =80 \\ 5x = 5 \times 20 = 100 \:and \:7x = 7 \times 20 = 140$

Answer 2

Answer:

Let's the measures in the ratio be

Hence

angleA + angleB + angleC + angleD = 360°

2x +4x +5x + 7x = 360°

6x +12x = 360°

18x = 360°

x =360/18

x = 20°

therefore

angleA = 2x = 2(20) = 40

angleB = 4x =4(20) = 80

angleC = 5x = 5(20) = 100

angleD = 7x = 7(20)= 140