Exercise 12 Page 358

Now we can rewrite this equation to obtain the expression for m ∠ 3. m∠ 3 + (25x+19) ^(∘) = 180^(∘) [0.4em] ⇕ [0.4em] m∠ 3 = [180 - (25x+19)] ^(∘) To find the measure of ∠ 3, we will find the value of x. Let's start by recalling that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Next we will recall the definitions of an exterior angle and its remote interior angles.

1. An exterior angle of a triangle is an angle formed by a side and extension of an adjacent side.
2. For each exterior angle of a triangle, the two nonadjacent interior angles are its remote interior angles.

In this case, ∠ 4 is an exterior angle. Let's mark its remote interior angles on the diagram!