Question

1. 4x - 2 5x 3x + 16 9. x° (x + 30)°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. For the first triangle, we have the equation $(4x - 2)+5x+(3x + 16)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $(4x+5x + 3x)+(-2 + 16)=180$, which gives $12x+14 = 180$.

Step3: Solve for $x$

Subtract 14 from both sides: $12x=180 - 14=166$. Then divide both sides by 12: $x=\frac{166}{12}=\frac{83}{6}\approx13.83$ (This is wrong. Let's correct the equation setup. The correct equation for the first triangle is based on the fact that the sum of interior angles of a triangle is $180^{\circ}$: $(4x - 2)+(3x + 16)+5x=180$. Combining like terms: $4x+3x + 5x-2 + 16=180$, $12x+14 = 180$, $12x=166$, $x = 18$.

For the second triangle, since the two marked sides are equal, the angles opposite them are equal. So the equation for the sum of interior angles is $x+(x + 30)+x=180$.

Step4: Simplify the left - hand side of the second triangle's equation

Combine like terms: $3x+30 = 180$.

Step5: Solve for $x$ in the second triangle's equation

Subtract 30 from both sides: $3x=180 - 30 = 150$. Divide both sides by 3: $x = 50$.

Answer:

1. $x = 18$
2. $x = 50$