1. **Problem statement:** Find the value of $x$ in the given triangles. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. ### (a) Triangle angles: $(2x + 20)^\circ$, $70^\circ$, $80^\circ$ 3. Write the equation for the sum of angles: $$ (2x + 20) + 70 + 80 = 180 $$ 4. Simplify the equation: $$ 2x + 20 + 150 = 180 $$ $$ 2x + 170 = 180 $$ 5. Solve for $x$: $$ 2x = 180 - 170 $$ $$ 2x = 10 $$ $$ x = \frac{10}{2} = 5 $$ ### (b) Triangle angles: $130^\circ$, $(6x - 7)^\circ$, $(x + 15)^\circ$ 6. Write the equation for the sum of angles: $$ 130 + (6x - 7) + (x + 15) = 180 $$ 7. Simplify the equation: $$ 130 + 6x - 7 + x + 15 = 180 $$ $$ 7x + 138 = 180 $$ 8. Solve for $x$: $$ 7x = 180 - 138 $$ $$ 7x = 42 $$ $$ x = \frac{42}{7} = 6 $$ **Final answers:** - (a) $x = 5$ - (b) $x = 6$