1. **State the problem:** We are given a triangle XYZ with angles labeled as follows: angle X = $x + 2$, angle Y = $2x + 23$, and angle Z = $3x + 5$. We need to find the value of $x$ and the measures of each angle. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180 degrees. This gives us the equation: $$ (x + 2) + (2x + 23) + (3x + 5) = 180 $$ 3. **Combine like terms:** $$ x + 2 + 2x + 23 + 3x + 5 = 180 $$ $$ (x + 2x + 3x) + (2 + 23 + 5) = 180 $$ $$ 6x + 30 = 180 $$ 4. **Solve for $x$:** $$ 6x = 180 - 30 $$ $$ 6x = 150 $$ $$ x = \frac{150}{6} = 25 $$ 5. **Find each angle measure:** - Angle X: $x + 2 = 25 + 2 = 27$ degrees - Angle Y: $2x + 23 = 2(25) + 23 = 50 + 23 = 73$ degrees - Angle Z: $3x + 5 = 3(25) + 5 = 75 + 5 = 80$ degrees 6. **Check the sum:** $$ 27 + 73 + 80 = 180 $$ which confirms our solution is correct. **Final answer:** $x = 25$, angles are 27°, 73°, and 80° respectively.