1. **Stating the problem:** Given a triangle with angles \(\angle D = 134^\circ\) (exterior angle), \(\angle A = 62^\circ\), and \(\angle B = 25^\circ\), find the unknown interior angle \(\angle D\) of the triangle. 2. **Formula and rules:** The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. Mathematically, for exterior angle \(\angle D_{ext}\), $$\angle D_{ext} = \angle A + \angle B$$ 3. **Apply the theorem:** Substitute the known values: $$134^\circ = 62^\circ + 25^\circ$$ 4. **Calculate the sum of interior opposite angles:** $$62^\circ + 25^\circ = 87^\circ$$ 5. **Check consistency:** Since the exterior angle \(134^\circ\) should equal the sum of the two opposite interior angles, but \(87^\circ \neq 134^\circ\), this suggests the given \(134^\circ\) is the exterior angle at vertex D, and the interior angle \(\angle D\) is supplementary to it. 6. **Find interior angle \(\angle D\):** Interior and exterior angles at the same vertex sum to \(180^\circ\), so $$\angle D = 180^\circ - 134^\circ = 46^\circ$$ 7. **Verify sum of interior angles:** $$\angle A + \angle B + \angle D = 62^\circ + 25^\circ + 46^\circ = 133^\circ$$ This is less than \(180^\circ\), so there might be a misinterpretation or missing information, but based on the exterior angle theorem and given data, the interior angle at D is \(46^\circ\).