The angles of a triangle are a, b and 50∘.
If the difference a - b is 40∘, then what is the value of a?
Solving using b
So we know that all angles in a triangle add up to 180°.
The equation we get is 50°+a+b=180°
Because there are two variables, we need to equations, and the other is already given. Which is a-b=40
We can use substitution and get 50°+(b+40°)+b=180°.
Just add and subtract a few things to get 2b=90°, and b=45°
We can take b back into the equation and get a=85°.
Solving using a
If we want to solve using a, we can substitute b=a-40 into the first equation.
We get 50°+2a-40°=180°. 2a=170° and a=85°.