1. **Problem statement:** Given a triangle with one angle measuring 122° and two sides marked as equal, find the measure of Angle 1. 2. **Understanding the problem:** The triangle has an angle of 122° and two sides marked equal, indicating an isosceles triangle. The equal sides imply the angles opposite those sides are equal. 3. **Formula and rules:** The sum of angles in any triangle is always $$180^\circ$$. 4. **Step-by-step solution:** - Let Angle 1 be $$x$$. - Since the triangle is isosceles with two equal sides, the two base angles are equal. One of these is Angle 1 ($$x$$), so the other base angle is also $$x$$. - The third angle is given as $$122^\circ$$. 5. **Write the angle sum equation:** $$x + x + 122 = 180$$ 6. **Simplify:** $$2x + 122 = 180$$ 7. **Isolate $$x$$:** $$2x = 180 - 122$$ $$2x = 58$$ 8. **Divide both sides by 2:** $$\cancel{2}x = \frac{58}{\cancel{2}}$$ $$x = 29$$ 9. **Answer:** The measure of Angle 1 is $$29^\circ$$. This means the two equal angles in the isosceles triangle are each 29 degrees, and the third angle is 122 degrees, summing to 180 degrees as expected.