Question

Franklin measured and labeled the angles of a triangle as shown. Jennifer says that at least one of his measures is incorrect. Explain in at least two different ways how Jennifer knows that this is true

Answer 1

Explanation 1:

Jennifer knows that at least one of Franklin's measures of the angles of the triangle is incorrect because the sum of the inner angles of a triangle is equal to 180°.

When you add the shown measures you get:

• 37° + 97° + 134° =  268° ≠ 180°, which makes this an impossible triangle.

Explanation 2:

Jennifer also can know that either the measure 97° or 134° (or even both) is incorrect.

This is so because the addition of those two measures is

• 97° + 134° = 231°

Since 231° > 180° those measures cannot be correct because the sum  of two angles of an triangle has to be less than 180°, given that when they are summed to the other angle the sum has to be 180°.