Question

please answer ..............

in the adjioning figure EF equals to EC
then find value of x

Answer 1

In the given figure, it is given that,

EF = EC


So their opposite angles will be equal.

=> angle EFC = angle ECF

Let, angle ECF = angle EFC = y

So in ∆EFC by angle sum property of triangle,

x + angle EFc + angle ECF = 180°

=> x + y + y = 180°

=> 2y + x = 180°

=> 2y = 180 - x

=> y = (180 - x)/2

=> y = 90 - x/2


Now we know that, angle ECF = y

=> angle ECF = 90 - x/2


Now in the given figure,
angle ABC = angle AbE + angle EBC

=> angle ABC = x + x (given)

=> angle ABC = 2x

Again, in ∆ABC by angle sum property,

we have

angle BAC + angle ABC + angle ACB = 180°

and angle ACB = angle ECF (because they coincide with each other)

=> x + 2x + angle ECF = 180°

=> x + 2x + 90 - x/2 = 180°

=> 3x - x/2 = 180 - 90

=> (6x - x)/2 = 90°

=> 5x/2 = 90°

=> x = 90 × 2/5

=> x = 36°


Hope it helps dear friend ☺️✌️✌️

Answer 2

A+B+C=180 then 2x+x+C=180
3x+C=180
F=C
X+F+C=180 then x+2C=180
2X=C
Therefore 5X=180
X=36