Question

Based on informationen in the
figure, prove x=a+b+c​

Answer 1

Answer:

In △ ABD ∠ A + ∠ B + ∠ D = 180 °

Angle Sum Property b + c + ∠ OBD + a + ∠ ODB = 180 °

∠ OBD + ∠ ODB = 180 ° - a - b - c

Now , In △ OBD ∠ OBD + ∠ ODB + ∠ BOD = 180 ° Angle Sum Property 180 ° - a - b - c + x = 180 ° x = 180 ° - 180 ° + a + b + c x = a + b+ c

Hence Proved .

Answer 2

Step-by-step explanation:

let angle opposite to x be y

since it is a quadrilateral,

a+b+c+y=360°-----1

also, x and y are opposite angles, so x+y=360°---2

from 1,we get y=360-a-b-c

put that in 2

x+360-a-b-c=360

x+360-360-a-b-c=0

x-a-b-c=0

x=a+b+c

hence proved

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