Focus on the triangle with angle ∠ 5 as one of its exterior angles.
85^(∘)
Let's label all angles and concentrate on the triangle with angle ∠ 5 as one of its exterior angles.
We are asked to find the measure of this exterior angle. Notice, that the measure of the two remote interior angles of this triangle are given. The Exterior Angle Theorem states a connection between these measures.
m∠ 5=m∠ 8+m∠ 9
We can find m∠ 5 by substituting the given m∠ 8=57^(∘) and m∠ 9=28^(∘) in this equation.
