- Angle a: 72°, Reason: Alternate angles are equal.
- Angle b: 113°, Reason: Co-interior angles sum to 180°.
- Angle c: 126°, Reason: Corresponding angles are equal.
- Angle d: 7°, Reason: Angles on a straight line sum to 180°; 180° - (68° + 75°) = 37°, then 180° - (81° + 39° + 37°) = 23°, but corrected for direct calculation: 180° - 68° - 75° = 37°, and since d is adjacent to 37° on a straight line, d = 180° - 37° - 136°? Wait, recalculating: the triangle has angles 68°, 75°, so third angle is 37°, and d is vertically opposite or adjacent? Actually, d is part of the straight line with 68° and 75°, so d = 180° - 68° - 75° = 37°? But the diagram shows d as an exterior angle. Rechecking: if the triangle has angles 68° and 75°, the third interior angle is 37°, and d is adjacent to it on a straight line, so d = 180° - 37° = 143°? No, that doesn't match. Let me correct: in the diagram, d is at the top, with 68° and 75° in the triangle. The angle next to d inside the triangle is 180° - 68° - 75° = 37°, and since d and this 37° are on a straight line, d = 180° - 37° = 143°. But earlier I thought it was 7°, which is wrong. Correct answer: Angle d: 143°, Reason: Angles in a triangle sum to 180°, so the third angle is 37°, and angles on a straight line sum to 180°, so d = 180° - 37° = 143°.
- Angle e: 81°, Reason: Vertically opposite angles are equal.
- Angle f: 60°, Reason: Angles in a triangle sum to 180°; 180° - 81° - 39° = 60°.
- Angle g: 85°, Reason: Angles in a triangle sum to 180°; 180° - 21° - 74° = 85°.
Parent Tip: Review the logic above to help your child master the concept of between the lines math worksheet.
