Question

Complete the proof of the exterior angle theorem. Given: 4 is an exterior angle of ABC. Prove: m1 + m2 = m4. Statement Reason 1. 4 is an exterior angle of ABC. 1. 2. 3 and 4 form a linear pair. 2. 3. 3 is supplementary to 4. 3. 4. m3 + m4 = 180°. 4. 5. 5. Triangle sum theorem. 6. m1 + m2 + m3 = m3 + m4. 6. 7. 7.

Answer 1

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this case, we are asked to prove that m1 + m2 = m4.

Step-by-step explanation:

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this case, we are given that angle 4 is an exterior angle of triangle ABC. To prove that m1 + m2 = m4, we can use the following steps:

1. Given: 4 is an exterior angle of ABC.
2. 3 and 4 form a linear pair.
3. 3 is supplementary to 4.
4. m3 + m4 = 180° (by definition of supplementary angles).
5. Triangle sum theorem (states that the sum of the measures of the three angles in a triangle is 180°).
6. m1 + m2 + m3 = m3 + m4 (substituting m3 + m4 from step 4).
7. m1 + m2 = m4 (subtracting m3 from both sides).