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Goshia [24]
3 years ago
9

Answer ASAP, Will give brainliest

Mathematics
1 answer:
erastova [34]3 years ago
7 0

Answer:

Step-by-step explanation:

1) ABCD is a trapezium. AB ║ CD

∠ADC + ∠DAB  = 180°  { Co interior angles}

110° + ∠DAB = 180

         ∠DAB = 180 -110

∠DAB = 70°

2) Sum of all angles of trapezium = 360°

∠A + ∠B + ∠DCB + ∠D = 360

70° + 50° + ∠DCB + 110° = 360

                 230 + ∠DCB = 360

                            ∠DCB = 360 - 230

∠DCB = 130°

3) For finding the height, use Pythagorean theorem

height² + base² = hypotenuse²

      height² + 6² = 10²

      height² + 36 =100

               height² = 100 - 36

              height² = 64

               height = √64

height = 8 m

4) a = AB = x m

  b = 9 m

h = height = 8 m

Area of trapezium = 120 m²

\frac{(a+b)*h}{2}\\\\  = 120

\frac{(x+9)*8}{2} =120\\\\\\(x +9)*4 = 120

x + 9 = 120/4

x + 9 = 30

    x = 30 - 9

x = 21 m

AB = 21m

                             

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