Answer and Explanation:
We know that the interior angles of a triangle add to 180°.
So, we can construct the following equation to solve for x:
[tex]65\° + (3x-10)\° + (2x)\° = 180\°[/tex]
↓ combining like terms
[tex]55\° + (5x)\° = 180\°[/tex]
↓ subtracting 55° from both sides
[tex](5x)\° = 125\°[/tex]
↓ dividing both sides by 5°
[tex]\boxed{x = 25}[/tex]
Next, we can plug this x-value into the definitions of angles B and C:
[tex]m\angle B = (3x-10)\°[/tex]
[tex]m\angle B = (3(25)-10)\°[/tex]
[tex]m\angle B = (75-10)\°[/tex]
[tex]\boxed{m\angle B = 65\°}[/tex]
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[tex]m\angle C = (2x)\°[/tex]
[tex]m\angle C = (2(25))\°[/tex]
[tex]\boxed{m\angle C = 50\°}[/tex]
