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McGraw Hill Integrated II, 2012 View details

1. Angles of Triangles

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Exercise 5 Page 339

Look for interior and exterior angles.

49 ^(∘)

Practice makes perfect

Consider the given diagram that represents the triangle formed by the brace and the rest of the frame of a deck chair.

We are given the measures of an exterior angle and two remote interior angles. We are asked to find the measure of the other remote interior angle. To do so, we will use the Exterior Angle 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 theorem this to set up and solve an equation for m∠ 4. m∠ 4 + m∠ 3 = m∠ 1 Now we will substitute m∠ 1= 102^(∘) and m∠ 3= 53^(∘) into the equation and solve it for m∠ 4. Let's do it!

m∠ 4+m∠ 3=m∠ 1

SubstituteII

m∠ 1= 102^(∘), m∠ 3= 53^(∘)

m∠ 4+ 53^(∘)= 102^(∘)

SubEqn

LHS-53^(∘)=RHS-53^(∘)

m∠ 4=49^(∘)

The measure of ∠ 4 is 49^(∘).