Find a solution to a problem by forming an equation and solving it
Maths can be really useful because you can simplify problems by picking out what is really important, making it easier to solve.
It is possible to describe situations using by creating maths equations and using algebra. Once we have something in the form of an equation, we have a range of tools for solving it.
An isosceles triangle has three angles – angle 1, angle 2 and angle 3. Angle 2 is twice the size of angle 3. What is the size of all three angles? What else is special about this triangle?
Well, we know that in an isosceles triangle, two angles are the same. Since angle 2 is bigger than angle 3, we know that angles 3 and 1 must be the identical angles. We don’t know how big they are yet though, so we can just say they’re both ‘x’ degrees big.
Angle 1 = x Angle 3 = x
Angle 2 is twice the size of angle 3, so even though we don’t know how big either of them are, we can still say this:
Angle 2 = 2x
Now, we know that all three angles have to sum to 180 degrees. So we just write that out the maths question as:
x + 2x + x = 180
4x = 180
Now to finally solve the equation all we must do is simplify the above answer:
x = 45
So x is 45 degrees. Now we know that angles 1 and 3 must both be 45 degrees, and angle 2 is 90 degrees. The solution to the second part of the question is that the triangle is a right angled triangle.
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