Question

lesson 7: triangles
classifying triangles by angle measurement
by definition, an obtuse triangle has ______
a. one angle greater than 180 degrees
b. one angle greater than 90 degrees
c. all angles less than 90 degrees
d. one angle equal to 90 degrees

Explanation:

To solve this, we recall the definition of an obtuse triangle. An obtuse triangle is defined as a triangle that has one angle greater than 90 degrees (and less than 180 degrees, since the sum of angles in a triangle is 180 degrees). Let's analyze each option:

• Option a: A triangle's angle cannot be greater than 180 degrees because the sum of all three angles in a triangle is 180 degrees. So this is incorrect.
• Option b: This matches the definition of an obtuse triangle (one angle greater than 90 degrees).
• Option c: A triangle with all angles less than 90 degrees is an acute triangle, not obtuse. So this is incorrect.
• Option d: A triangle with one angle equal to 90 degrees is a right triangle, not obtuse. So this is incorrect.

Answer:

b. one angle greater than 90 degrees