The angles of a triangle are a, b and 50∘.

If the difference a - b is 40∘, then what is the value of a?


 Jul 29, 2020

a-b = 40     so   b = a-40


then     a      +   a-40     + 50      = 180        solve for 'a'

 Jul 29, 2020

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°.

 Jul 29, 2020

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