Question

in the given figure prove that x=a+b+c

Answer 1

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

PLEASE REFER TO THE PICTURE FOR THE FIGURE

ANSWER

x = a + b + c

GIVEN

∠BAC = a

∠ACB = c

∠CBA = b

TO PROVE

x = a+b+c

SOLUTION

We can simply solve the above problem as follows;

First, We will produce AD to E such that,

Line segment AE is the angle bisector of ∠BDC and ∠BAC

Let,

∠BAE = ∠1

∠CAE = ∠2

∠BDE = ∠3

∠CDE = ∠4

So,

∠1 + ∠2 = ∠a

∠3 + ∠4 = x (Equation 1)

Also,

∠b + ∠1 = ∠3 (Equation 2)

And,

∠c + ∠2 = ∠4 (Equation 2)

(Exterior angle = sum of interior opposite angles.)

Adding Equation 2 and 3

∠3 + ∠4 = ∠1 + ∠2 + b + c

Form equation 1

x = a + b + c

= a + b + c Hence, Proved

= a + b + c Hence, Proved#Spj2