Question

What is the value of y?



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y =

Answer 1

y=40............................................

Answer 2

Answer : The value of 'x' and 'y' is,
`8^o` and
`40^o` respectively.

Step-by-step explanation :

As we know that the sum of interior angles of a triangle is equal to
`180^o`.

`\angle A+\angle B+\angle C=180^o`

Given:

`\angle A=(2y+20)^o`

`\angle B=(5x)^o`

`\angle C=40^o`

`\angle A+\angle B+\angle C=180^o`

Now put all the given value of angle in the above expression, we get:

`(2y+20)^o+(5x)^o+40^o=180^o`

`(2y)^o+20^o+(5x)^o+40^o=180^o`

`(2y)^o+(5x)^o+60^o=180^o`

`(2y)^o+(5x)^o=180^o-60^o`

`(2y)^o+(5x)^o=120^o` ...............(1)

The given triangle is an isosceles triangle in which the angles opposite to equal sides are always equal.

Thus,
`\angle B=\angle C`

`(5x)^o=40^o`

`x=(40)/(5)`

`x=8^o`

Now put the value of 'x' in equation 1, we get the value of 'y'.

`(2y)^o+(5x)^o=120^o`

As,
`(5x)^o=40^o`

So,
`(2y)^o+40^o=120^o`

`(2y)^o=120^o-40^o`

`(2y)^o=80^o`

`y=(80)/(2)`

`y=40^o`

Thus, the value of 'x' and 'y' is,
`8^o` and
`40^o` respectively.