Answer:
- 180°
- consecutive interior angles are supplementary
- ∠6
- 20°, 160°
Explanation:
The blanks get filled in like this:
Statement 3: m∠6 +m∠4 = 180°
Reason 3: Consecutive interior angles are supplementary
Statement 4: m∠6 +8·m∠6 = 180°
Statement 5: m∠6 = 20°, m∠4 = 160°
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You can see from the diagram that angles 4 and 6 are consecutive interior angles. You know the relation between those angles is that they are supplementary. The problem is asking you to state that relationship as Reason 3.
The given relation between the angles, m∠6 = 1/8·m∠4, can be recast as ...
8·m∠6 = m∠4
This is the substitution that is used in statement 4.
Simplifying that statement gives 9·m∠6 = 180° ⇒ m∠6 = 180°/9 = 20°. Then m∠4 = 8·m∠6 = 8·20° = 160°.