1. **State the problem:** We have two intersecting lines forming four angles. One angle is 64°, another angle y is 90°, and we need to find the measure of angle x. 2. **Recall important rules:** - Vertical angles are equal. - Adjacent angles on a straight line sum to 180°. - A right angle is 90°. 3. **Analyze the given information:** - Angle y is given as 90°. - Angle adjacent to y and x are on a straight line, so their sum is 180°. 4. **Find angle x:** Since y = 90°, and x is adjacent to y on a straight line, $$x + y = 180$$ $$x + 90 = 180$$ Subtract 90 from both sides: $$x = 180 - 90$$ $$x = 90$$ 5. **Find the missing angle opposite 64°:** Vertical angles are equal, so the angle opposite 64° is also 64°. 6. **Summary:** - $x = 90°$ - $y = 90°$ (given) - The angle opposite 64° is 64° (vertical angles) Final answer: $$x = 90°$$ $$y = 90°$$