Question

In the following figure find `m/_x`?

Answer 1

Image reference...
Answer`=36^@`

Explanation:

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Answer 2

`color(red)(X = 36^0`

Explanation:

`/_(BAC) = /_(ACD) = /_(ABC) = X` as

`color(red)(AD = DC = BC)`

`/_(BDC) = /_(DAC) + /_(DCA) = 2X`

Exterior angle = sum of the interior opposite angles

`/_(BDC) = /_(BCD) = 2X` as

`color(red)(BC = BD)`

In triangle BDC,
`/_(DBC) + /_(BCD) + /_(BDC) = 180^0`

I. e. `X + 2X + 2X = 180^0`

`X = 180 / 5 = 36^0`

`color(red)(X = 36^0`

Answer 3

`m/_x=36^@`

Explanation:

Let us name the points in the diagram as follows:

As `DeltaBCD` is isoscoles triangle, we have

`m/_DCB=m/_DBC=x`

and as exterior angle of a triangle is always equal to sum of intereor opposite angles

`m/_ADC=x+x=2x`

Again as `DeltaADC` is isoscels triangle abd hence `m/_ACD=m/_ADC=2x`

and hence `m/_A=180^@-2x-2x=180^@-4x`

Also `m/_ACB=m/_DCB+m/_ACD=x+2x=3x`

Now as `AC=BC` we have `m/_A=m/_B=x` and hence

in `DeltaABC`, the three angles are `x,x` and `3x` and we have

`x+x+3x=180^@` or `5x=180^@` or `x=36^@`