Question

9. Write an equation relating the measures of

Answer 1

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°

__

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

__

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.