Here a right angled triangle given. We know that one angle of a right angled triangle is 90°.
As the sum of three angles of a triangle is 180°, so we can say the sum of other two angles of a right angled triangle is (180-90)° = 90°.
Here in the figure the other two angles given [tex] (2x)^o [/tex] and [tex] (x+15)^o [/tex]. Sum of these two angles is 90°.
So we can write the equation as,
[tex] (2x)+(x+15) = 90 [/tex]
We have to remove the parenthesis now.
[tex] 2x+x+15 = 90 [/tex]
Now we will add the like terms. Here x and 2x are like terms. By adding them we will get,
[tex] 3x+15 = 90 [/tex]
To solve it for x, now we have to move 15 to the other side by subtracting it from both sides.
[tex] 3x+15-15 = 90-15 [/tex]
[tex] 3x= 90-15 [/tex]
[tex] 3x= 75 [/tex]
Now to get x, we have to move 3 to the other side, by dividing it to both sides.
[tex] (3x)/3 = (75)/3 [/tex]
[tex] x = (75)/3 [/tex]
[tex] x = 25 [/tex]
We have got the required value of x.
The solution is x= 25.
