Chapter 10, Start of Chapter, Activity, Exercise 4

# Place the third angle as shown. What does this tell you about the sum of the measures of the angles?

### Explanation

• In a straight line, the sum of the measures of the angles add up to 180 degrees. This means that if you have a, b, and c angles, the sum of those angles would be 180 degrees. If, on the other hand, you have a triangle, then the total of its angles will be closer to 360 degrees, as the sum of its angles is equal to the sum of the angles formed by adding the angles formed by two straight lines.
• All three of a triangle's angles add up to 360 degrees. Consequently, the sum of the angles in a triangle is 360 degrees, but the sum of the angles in a straight line is less than 180 degrees, because the triangle's total angles are equal to the total angles of another straight line minus the sum of the angles in a straight line. This deviation is exactly 180 degrees.
• All the angles of a triangle add up to 360 degrees, but all the angles in a line add up to just 180 degrees. That's a 180-degree swing between the two amounts. The reason for this dissimilarity is because the sum of the angles in a triangle is greater than the total of the angles in a straight line plus a triangle.