1. **State the problem:** We need to find the measures of angles 1, 2, 3, and 4 in a right triangle where angle 2 is given as 35° and the right angle is at the bottom left corner. 2. **Recall important rules:** - The sum of angles in any triangle is 180°. - A right angle measures 90°. - Adjacent angles on a straight line sum to 180°. 3. **Given:** - $m\angle 2 = 35^\circ$ - $m\angle 3 = 90^\circ$ (right angle) 4. **Find $m\angle 1$:** Since angles 1, 2, and 3 are the three angles of the triangle, $$m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ$$ Substitute known values: $$m\angle 1 + 35^\circ + 90^\circ = 180^\circ$$ Simplify: $$m\angle 1 + 125^\circ = 180^\circ$$ Subtract 125° from both sides: $$m\angle 1 = 180^\circ - 125^\circ = 55^\circ$$ 5. **Find $m\angle 4$:** Angle 4 is adjacent to angle 3 on a straight line, so: $$m\angle 3 + m\angle 4 = 180^\circ$$ Substitute $m\angle 3 = 90^\circ$: $$90^\circ + m\angle 4 = 180^\circ$$ Subtract 90° from both sides: $$m\angle 4 = 90^\circ$$ **Final answers:** $$m\angle 1 = 55^\circ, \quad m\angle 2 = 35^\circ, \quad m\angle 3 = 90^\circ, \quad m\angle 4 = 90^\circ$$