Angle Measures A2B1D4

1. **State the problem:** We have a rectangle with two diagonals crossing, forming four angles at the intersection. One of these angles is given as $67^\circ$. We need to find the measures of angles $m\angle 1$, $m\angle 2$, and $m\angle 3$. 2. **Recall properties:** The diagonals of a rectangle are equal and bisect each other, and the intersection forms vertical angles and supplementary angles. 3. **Identify angles:** The given $67^\circ$ angle is adjacent to $m\angle 1$ and vertical to $m\angle 3$. Since vertical angles are equal, $m\angle 3 = 67^\circ$. 4. **Find $m\angle 1$:** $m\angle 1$ and the $67^\circ$ angle are supplementary because they form a straight line. $$m\angle 1 + 67^\circ = 180^\circ$$ $$m\angle 1 = 180^\circ - 67^\circ = 113^\circ$$ 5. **Find $m\angle 2$:** $m\angle 2$ is vertical to the $67^\circ$ angle on the left side, so $$m\angle 2 = 67^\circ$$ **Final answers:** $$m\angle 1 = 113^\circ$$ $$m\angle 2 = 67^\circ$$ $$m\angle 3 = 67^\circ$$