Answers:
x = 12angle A = 35angle ABC = 65
Explanation:
Let y be the measure of angle ABC.
We can see that y = 4x+17 because the two angles (y and 4x+17) are vertical angles. Vertical angles are always congruent.
From here, focus entirely on the interior angles of triangle ABC.
Recall that for any triangle, the interior angles always add to 180
A+B+C = 180
(x+23)+(y)+(80) = 180 plug in the given angle measures
(x+23)+(4x+17)+(80) = 180 replace y with 4x+17
5x+120 = 180 combine like terms
5x = 180-120 subtract 120 from both sides
5x = 60
x = 60/5 divide both sides by 5
x = 12
Now use that x value to find the following:
angle A = x+23 = 12+23 = 35angle ABC = y = 4x+17 = 4*12+17 = 48+17 = 65
In short we have this summary of values we found:
x = 12angle A = 35angle ABC = 65