[tex]\boxed{x=29} \\ \\ \\ \boxed{y=51}[/tex]
Explanation:
As you can see from the figure, we have a triangle that has two equal sides. This is indicated with the two small lines in each side. If so, the angle opposite to each of these sides measure the same. Therefore, it is true that the missing angle measures:
[tex](x-2)^{\circ}[/tex]
We also know that the sum of the internal angles in every triangle equal 180°. So:
[tex](x-2)^{\circ}+(x-2)^{\circ}+(4x+10)^{\circ}=180^{\circ} \\ \\ x+x+4x-2-2+10=180 \\ \\ 6x+6=180 \\ \\ 6x=174 \\ \\ \boxed{x=29}[/tex]
Angles [tex](x-2)^{\circ} \ and \ 3y^{\circ}[/tex] are supplementary, so:
[tex](x-2)^{\circ}+3y^{\circ}=180^{\circ} \\ \\ \\ But \ x=29: \\ \\ 29-2+3y=180 \\ \\ 27+3y=180 \\ \\ 3y=180-27 \\ \\ 3y=153 \\ \\ \boxed{y=51}[/tex]
Learn more:
Area of a triangle: https://brainly.com/question/9835350
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