Answers:
- x = 12
- angle A = 35
- angle ABC = 65
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Step-by-step 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.
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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 = 35
- angle ABC = y = 4x+17 = 4*12+17 = 48+17 = 65
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In short we have this summary of values we found:
- x = 12
- angle A = 35
- angle ABC = 65