1. **State the problem:** We need to find the measure of angle 1, denoted as $m\angle 1$, in a triangle where two other angles are given as 87° and 46°. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always 180°. This can be written as: $$m\angle 1 + 87^\circ + 46^\circ = 180^\circ$$ 3. **Set up the equation:** Substitute the known angles: $$m\angle 1 + 87 + 46 = 180$$ 4. **Simplify the sum of known angles:** $$87 + 46 = 133$$ So the equation becomes: $$m\angle 1 + 133 = 180$$ 5. **Solve for $m\angle 1$:** $$m\angle 1 = 180 - 133 = 47$$ 6. **Conclusion:** The measure of angle 1 is 47°. Therefore, $m\angle 1 = 47^\circ$.