Exercise 3 Page 473

We are given a triangle with one exterior angle marked on a picture of a speed skater. An exterior angle of a triangle is an angle formed by one side of the triangle and the extension of the adjacent side. We want to find the measure of ∠ 1. Let's take a look at the given picture.

As we can see, the angle of measure 126^(∘) is an exterior angle. Moreover, this angle and ∠ 1 form a linear pair. Recall that a linear pair is a pair of adjacent angles with non-common opposite sides. To find m∠ 1, we can use the Supplement Theorem.

Supplement Theorem

If two angles form a linear pair, then they are supplementary angles.

We can illustrate this theorem with an example.

Remember that the measures of two supplementary angles always have a sum of 180^(∘) as together they create a straight angle. We know that ∠ 1 and the angle of measure 126^(∘) form a linear pair. Therefore, we can write that the sum of the measures of these angles is equal to 180^(∘).

m∠ 1+ 126=180

SubEqn

LHS-126=RHS-126

m∠1=180-126

SubTerm

Subtract term

m∠1=54

The measure of ∠ 1 is 54^(∘).