Question

from the adjoining figure, the value of x+y is
a) 270
b) 240
c) 360-120
d) 360-90​

Answer 1

Answer:

Step-by-step explanation:

∠BAD + 130 = 180   {Linear pair}

∠BAD = 180 - 130 = 50

∠BAD + ∠ADB = 130   {Exterior angle equals sum of opposite interior angles}

50 + ∠ADB = 130

        ∠ADB = 130 - 50= 80

∠ADB + x = 180 {Linear pair}

80 + x = 180

       x = 180 - 80

x = 100

ΔADC is an isosceles triangle. So, ∠DAC = ∠ACD = z

In ΔADC,

x + z + z = 180

x +2z = 180

100 + 2z = 180

  2z = 180 - 100 = 80

z = 80/2

z = 40

z + y = 180   {linear pair}

40 + y = 180

y = 180 - 40

y = 140

x + y = 100 + 140 = 240