1. **Stating the problem:** We are given four angles around two intersecting lines forming a triangle with one right angle. The measures are $m\angle 1 = 35^\circ$, $m\angle 2 = 55^\circ$, $m\angle 3 = 55^\circ$, and $m\angle 4 = 55^\circ$. We want to analyze these angles and verify their relationships. 2. **Understanding the setup:** The figure has two intersecting lines forming a right angle at $\angle 1$ (top). Angles 2 and 3 are adjacent on the horizontal line, and angle 4 is at the far right end on the horizontal line. The given angles inside the figure are $70^\circ$ between angles 1 and 4, and $35^\circ$ at the bottom left corner adjacent to angle 3. 3. **Key angle rules:** - The sum of angles around a point is $360^\circ$. - The sum of angles in a triangle is $180^\circ$. - Adjacent angles on a straight line sum to $180^\circ$. 4. **Check angle sums:** - Since $m\angle 1 = 35^\circ$ and it forms a right angle with the vertical line, the right angle is $90^\circ$. - Angles 2 and 3 are each $55^\circ$, so their sum is $110^\circ$. - Angle 4 is $55^\circ$. 5. **Verify triangle angles:** - The triangle formed includes angles 1, 2, and 3. - Sum: $35^\circ + 55^\circ + 55^\circ = 145^\circ$, which is less than $180^\circ$. - This suggests the right angle is not part of this triangle or there is an error in the given measures. 6. **Conclusion:** The given angle measures do not form a triangle with a right angle as described. The sum of angles 1, 2, and 3 is $145^\circ$, so the missing angle to complete $180^\circ$ would be $35^\circ$. **Final answer:** The sum of angles 1, 2, and 3 is $145^\circ$, so the missing angle in the triangle is $35^\circ$ to complete the $180^\circ$ total.