1. Stating the problem: We have a triangle intersected by two parallel lines, with angles given as 87°, 45°, and 36°, and we need to find the size of angle $x$. 2. Identify parallel line properties and angles: Since the lines are parallel, alternate interior angles and corresponding angles can be used to find unknown angles. 3. Use the fact that angles on a straight line sum to 180°: Consider the angles near $x$ and use their relationships to the given angles. 4. Analyze relationships: Angle adjacent to 45° in the triangle is supplementary; so its measure is $180° - 45° = 135°$. 5. Consider triangle angle sum: The triangle has interior angles that add to 180°, so group angles and use given values to find $x$. 6. Calculate $x$: Since $x$, 36°, and the angle adjacent to 45° (which is 135°) form a straight line or angle sum, the equation can be written as: $$x + 36° + 45° = 180°$$ Simplify: $$x + 81° = 180°$$ Subtract 81° from both sides: $$x = 180° - 81° = 99°$$ 7. Therefore, the size of angle $x$ is $99°$.