Question
Prove: m∠3 = 70°
Answers
GPT 3.5
Given information: ∠1 = ∠2 = 90° (right angles), m∠2 = 20° (given)
1. ∠1 and ∠2 are vertical angles as they share the same vertex and are not adjacent. Therefore, ∠1 = ∠2 (vertical angles are congruent).
2. Since ∠1 = ∠2 = 90°, this means m∠1 + m∠2 = 90° + 20° = 110°.
3. By the angle sum property of a triangle, the sum of the interior angles of a triangle is 180°.
4. Thus, m∠3 + m∠1 + m∠2 = 180°.
5. Substituting the known values, m∠3 + 110° = 180°.
6. m∠3 = 180° - 110° = 70°.
Therefore, m∠3 = 70°.
1. ∠1 and ∠2 are vertical angles as they share the same vertex and are not adjacent. Therefore, ∠1 = ∠2 (vertical angles are congruent).
2. Since ∠1 = ∠2 = 90°, this means m∠1 + m∠2 = 90° + 20° = 110°.
3. By the angle sum property of a triangle, the sum of the interior angles of a triangle is 180°.
4. Thus, m∠3 + m∠1 + m∠2 = 180°.
5. Substituting the known values, m∠3 + 110° = 180°.
6. m∠3 = 180° - 110° = 70°.
Therefore, m∠3 = 70°.