Exercise 6 Page 473

Let's begin with recalling the Triangle Angle Sum Theorem. The sum of the measures of the angles of a triangle is equal to 180^(∘).

Now, let's look at the given picture.

We can find m∠ 4 using the fact that the sum of the measures of all interior angles of a triangle is equal to 180^(∘).

m∠ 4+ 43^(∘)+ 34^(∘)=180^(∘)

AddTerms

Add terms

m∠4+77^(∘)=180^(∘)

SubEqn

LHS-77^(∘)=RHS-77^(∘)

m∠4=180^(∘)-77^(∘)

SubTerm

Subtract term

m∠4=103^(∘)