The measure of an angle exterior to angle F of triangle DEF measures 120°. Which of the following must be true?

Question

The measure of an angle exterior to angle F of triangle DEF measures 120&deg;. Which of the following must be true?

Accepted Answer

Since an angle exterior to angle F is 120&deg;, the measure of interior angle F is 60&deg;, and the sum of the measures of interior angles D and E is 120&deg;. Angles D and E could each measure 60&deg;, making triangle DEF acute and equilateral, but these angles could also measure 100&deg; and 20&deg; respectively, making triangle DEF obtuse and scalene. However, triangle DEF cannot be isosceles. Angle F measures 60&deg;; if either angles D or E measure 60&deg;, the other must also measure 60&deg;, making triangle DEF equilateral. Angles D and E cannot be congruent to each other without also being congruent to angle F. Therefore, triangle DEF can be acute, obtuse, scalene, or equilateral, but not isosceles.

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