Answer : The value of 'x' and 'y' is, [tex]8^o[/tex] and [tex]40^o[/tex] respectively.
Step-by-step explanation :
As we know that the sum of interior angles of a triangle is equal to [tex]180^o[/tex].
[tex]\angle A+\angle B+\angle C=180^o[/tex]
Given:
[tex]\angle A=(2y+20)^o[/tex]
[tex]\angle B=(5x)^o[/tex]
[tex]\angle C=40^o[/tex]
[tex]\angle A+\angle B+\angle C=180^o[/tex]
Now put all the given value of angle in the above expression, we get:
[tex](2y+20)^o+(5x)^o+40^o=180^o[/tex]
[tex](2y)^o+20^o+(5x)^o+40^o=180^o[/tex]
[tex](2y)^o+(5x)^o+60^o=180^o[/tex]
[tex](2y)^o+(5x)^o=180^o-60^o[/tex]
[tex](2y)^o+(5x)^o=120^o[/tex] ...............(1)
The given triangle is an isosceles triangle in which the angles opposite to equal sides are always equal.
Thus, [tex]\angle B=\angle C[/tex]
[tex](5x)^o=40^o[/tex]
[tex]x=\frac{40}{5}[/tex]
[tex]x=8^o[/tex]
Now put the value of 'x' in equation 1, we get the value of 'y'.
[tex](2y)^o+(5x)^o=120^o[/tex]
As, [tex](5x)^o=40^o[/tex]
So, [tex](2y)^o+40^o=120^o[/tex]
[tex](2y)^o=120^o-40^o[/tex]
[tex](2y)^o=80^o[/tex]
[tex]y=\frac{80}{2}[/tex]
[tex]y=40^o[/tex]
Thus, the value of 'x' and 'y' is, [tex]8^o[/tex] and [tex]40^o[/tex] respectively.
