Answer: A. $77$

Explanation:1. Understand the given information and the diagram (implied): In triangle RST: $\angle R = 11^{\circ}$ $\angle T = 77^{\circ}$ Point L lies on RS, point K lies on ST. Line segment LK is parallel to line segment RT ($LK \parallel RT$). We need to find the measure of angle SKL ($\angle SKL$).

2. Find the measure of angle S in triangle RST: The sum of angles in a triangle is $180^{\circ}$. $\angle R + \angle S + \angle T = 180^{\circ}$ $11^{\circ} + \angle S + 77^{\circ} = 180^{\circ}$ $88^{\circ} + \angle S = 180^{\circ}$ $\angle S = 180^{\circ} - 88^{\circ}$ $\angle S = 92^{\circ}$

3. Use the property of parallel lines and transversals: Since $LK \parallel RT$, and ST is a transversal line intersecting these parallel lines: Angle SKL and angle STR (which is $\angle T$) are corresponding angles. If two parallel lines are cut by a transversal, corresponding angles are equal. Therefore, $\angle SKL = \angle STR = \angle T$.

4. Substitute the value of angle T: $\angle T = 77^{\circ}$. So, $\angle SKL = 77^{\circ}$.

5. Alternative approach using similar triangles: Since $LK \parallel RT$, triangle SLK is similar to triangle SRT ($\triangle SLK \sim \triangle SRT$). This is because: - $\angle S$ is common to both triangles. - $\angle SLK = \angle SRT = \angle R$ (corresponding angles, RS is transversal). - $\angle SKL = \angle STR = \angle T$ (corresponding angles, ST is transversal). Since $\angle SKL = \angle T$, and $\angle T = 77^{\circ}$, then $\angle SKL = 77^{\circ}$.

6. Conclusion: The measure of angle SKL is $77$ degrees.