Angle Measure: m∠ 2=80 Definition: Definition of supplementary angles
Practice makes perfect
In this exercise we want to find the measure of ∠ 2 shown in the given diagram. Let's consider the given figure.
Angles ∠ 2, ∠ 3, and ∠ 6 form a linear pair. They are supplementary angles and, by definition, we know the sum of their measures is 180.
m∠ 2+m∠ 3+ m∠ 6=180
From the previous exercises, we know the measures of angles ∠ 3 and ∠ 6.
m∠ 3= 62
m∠ 6= 38
Let's substitute these measures into the equation and solve it for m∠ 2.
The measure of ∠ 2 is 80^(∘). To find it we used the definition of the supplementary angles.
Extra
Measures of ∠ 3 and ∠ 6
In this exercises we have used the measures of angles ∠ 3 and ∠ 6. These measures were found in the previous exercises. Let's consider the methods of finding these measures. We will find them one at a time.
m∠ 3
To find the measure of ∠ 3 we will use the measure given in the exercise, m∠ 11= 62.
To find the measure of ∠ 6 we will use another measure given in the exercise, m∠ 14= 38.
Angles ∠ 6 and ∠ 14 are corresponding angles. Therefore, from the Corresponding Angles Postulate we know that the measures of these angles are equal. This means that the measure of ∠ 6 is also 38^(∘).
