Answer:
4. m<7 = m<3 + m<2
Explanation:
Recall: the exterior angle theorem of a triangle states that an exterior angle is equal to the sum of the two opposite interior angles of a triangle.
❌Option 1 CANNOT be true
Rationale:
m<1 is an exterior angle of triangle ∆ABC and ∆EBC, so based on the exterior angle theorem of a triangle, m<1 = m<3 + m<4 or m<1 = m<ABC + m<5
❌Option 2 CANNOT be true.
Rationale:
m<5 ≠ m<3 - m<2
❌Option 3 CANNOT be true.
Rationale:
m<6 ≠ m<3 - m<2
✅Option 4 is CORRECT.
Rationale:
Based on the external angle theorem of a triangle,
m<7 = m<3 + m<2