Exercise 10 Page 339

We are given the measures of the interior angles of two triangles.

We are asked to find the measure of angle 3. To do so, notice that we are given an exterior angle and two remote interior angles of the triangle on the right.

We can use this information and the Exterior Angle Theorem to determine a relationship between these angles. Let's recall that theorem.

Exterior Angle Theorem

The measure of an exterior angle is the sum of the measures of the two remote interior angles.

We can use this theorem to set up and solve an equation for m∠ 3. Let's do it! m∠ 3+m∠ 4=m∠ 5 Now we will substitute 29^(∘) for m∠5 and 17^(∘) for m∠ 4 in the equation. Then we can solve it for m∠ 3 to find the measure of the missing angle. Let's do it!

m∠ 3+m∠ 4=m∠ 5

SubstituteII

m∠ 5= 29^(∘), m∠ 4= 17^(∘)

m∠ 3+ 17^(∘)= 29^(∘)

SubEqn

LHS-17^(∘)=RHS-17^(∘)

m∠ 3=12^(∘)

Therefore, the measure of ∠ 3 is 12^(∘).