Answer:
- ∠1 +∠2 +∠3 = 180°
- ∠1 +∠2 = ∠4
Step-by-step explanation:
The sum of the measures of the angles in a triangle is 180°. The equation relating angles 1, 2, 3 will reflect this fact.
m∠1 +m∠2 +m∠3 = 180°
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Of course, angle 3 is supplementary to angle 4, so we have ...
m∠3 +m∠4 = 180°
Substituting this expression for 180° in the first equation, we have ...
m∠1 +m∠2 +m∠3 = m∠3 +m∠4
Subtracting ∠3 from both sides, we are left with an equation relating angles 1, 2 and 4.
m∠1 +m∠2 = m∠4
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The "rule" expressing this last relationship is, "an exterior angle is equal to the sum of the remote interior angles." Knowing this relation can make a number of problems easier to solve.
