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Triangle $ABC$ is isosceles with base segment $AC$. If the measure of $A = 2x+y$, the measure of $B = y$, and the measure of $C = 3x+10$, how can I find $x$ and $y$ algebraically?

When I tried to solve this problem, I made all the measures of all the angles equal to $180 (2x+y+y+3x+10=180)$, then, simplified. I used substitution to plug what $y$ equals into the same equation - but, my base angles are not congruent.

What was the error I made in my solution that was incorrect?

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1 Answer 1

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$3x+10 = C = A = 2x+y \implies y = x + 10$

$\therefore 180 = A + B + C = 7x+30 \implies x = \frac{150}{7}$

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