Answer:
18°
Explanation:
Remember this:
All angles inside a triangle sum up to 180°.
So in your case:
∠A + ∠B + ∠C = 180°
Now you need to solve for ∠A, but you need to know what x is first. So we solve for it by plugging in the expressions into one equation. Let's start with what is given:
∠A = x -22
∠B = 3x + 19
∠C = x - 17
So we plug use the given and put it into our first equation so we can solve for x:
∠A + ∠B + ∠C = 180°
(x - 22) + (3x + 19) + (x - 17) = 180°
[tex](x - 22) + (3x + 19) + (x - 17) = 180\\\\ Combine\;like\;terms\\\\5x - 20 = 180\\\\Add\;20\;to\;both\;sides\;of\;the\;equation\\\\5x - 20 + 20 = 180 + 20\\\\5x = 200\\\\Divide\;both\;sides\;by\;5\\\\\dfrac{5x}{5}=\dfrac{200}{5}\\\\x = 40[/tex]
Now that we know that x = 40, we substitute that into the equation of ∠A.
∠A = x -22
∠A = 40 -22
∠A = 18°
