1. The problem: Construct a triangle given the base length and the two adjacent angles. 2. Given: Base $AB = 8$ cm, angle $A = 50^\circ$, angle $B = 60^\circ$. 3. Formula and rules: The sum of angles in a triangle is $180^\circ$. To construct the triangle, use a ruler and protractor. 4. Steps: - Draw base $AB$ of length 8 cm. - At point $A$, use a protractor to draw a ray making a $50^\circ$ angle with $AB$. - At point $B$, use a protractor to draw a ray making a $60^\circ$ angle with $BA$. - The intersection of these two rays is point $C$. - Connect $AC$ and $BC$ to complete triangle $ABC$. 5. Explanation: By constructing the two angles at the ends of the base, their rays intersect at the third vertex, ensuring the triangle has the given base and angles. Final answer: Triangle $ABC$ with base $AB=8$ cm, angle $A=50^\circ$, and angle $B=60^\circ$ constructed as described.