Triangle that deals in terms of a and b?

Question

What would be the correct way to approach this problem?

Answer 1

The unspecified angles in both the middle and bottom left triangles are $$(180-a-b)^\circ.$$ Hence, the unspecified angle in the top triangle is $$180^\circ-2(180-a-b)^\circ=(2a+2b-180)^\circ.$$ That angle together with $b^\circ$ and $c^\circ$ adds up to $180^\circ,$ so $$c=360-2a-3b.$$

There are other ways you could go about it, too.

Answer 2

Hints: The important facts to use are:

• The sum of the angles of any triangle $ = 180^\circ$.
• Supplementary angles add up to $180^\circ$

I'd recommend filling in the values of the missing, unidentified angles with its value, in terms of $a, b$, using the facts above, especially the ones that will help you determine the value of $c$ in terms of $a, b$.

You should obtain $c = 360 - 2a - 3b$.