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Use the relationship of vertical angles between lines that intersect.
123^(∘)
Let's consider the given diagram.
To find the measure of ∠ 6, we will first find m∠ 1. Recall that when two lines intersect, vertical angles are formed on opposite sides of the point of intersection, and these angles are always congruent.
Now, note that ∠ 2 and the angles with measure 80^(∘) and 43^(∘) form a straight line.
Therefore, the sum of their measures is 180^(∘). With this information, we can find the measure of ∠ 2. m∠ 2+43^(∘)+80^(∘)=180^(∘) ⇕ m∠ 2=57^(∘) Let's add this information to our diagram.
Next, we will find the measure of ∠ 3. We can use the fact that corresponding angles between parallel lines are congruent.
Since ∠ 2 and ∠ 3 are corresponding angles, they are congruent and therefore have the same measure. This means that m∠ 3 = 57^(∘). Let's add this information to our diagram.
Finally, note that ∠ 6 and ∠ 3, that measures 57^(∘), form a straight line.
These angles are supplementary and therefore the sum of their measures is 180^(∘). With this information, we can find the measure of ∠ 6. m∠ 6+57^(∘)=180^(∘) ⇕ m∠ 6=123^(∘)
