In triangle JKL, if m∠J < 90°, then ∠K and ∠L are __. Select all that apply.
Understand the Problem
The question is asking to determine the types of angles that angles K and L are in triangle JKL, given that angle J is less than 90 degrees. We need to analyze the properties of angles in a triangle to decide which characteristics apply to angles K and L.
Answer
The angles K and L are either both acute or one obtuse and one acute.
Answer for screen readers
The correct choices are:
- obtuse and acute or vice versa
- Both acute
Steps to Solve
-
Identify the properties of angles in a triangle
In triangle JKL, the sum of all angles must equal 180 degrees. Given that angle J is less than 90 degrees (acute), we can derive the possible types for angles K and L. -
Calculate the remaining angle
Since angle J is acute, let’s denote it as $m\angle J < 90^\circ$.
Thus, the sum of angles K and L can be expressed as:
$$ m\angle K + m\angle L = 180^\circ - m\angle J $$
This means that both angles K and L together must also be less than 180 degrees. -
Analyze the possibilities for angles K and L
Since the sum of K and L must be greater than 90 degrees but less than 180 degrees (as J is an acute angle), this implies that either K or L or both must be acute, thus we explore the types: -
Determine angle types
- If both angles K and L are less than 90 degrees, they are both acute.
- Alternatively, one could be less than 90 degrees (acute), and the other angle could be greater than 90 degrees (obtuse).
Thus, we can conclude that angles K and L can be classified as either both being acute, or one acute and one obtuse.
The correct choices are:
- obtuse and acute or vice versa
- Both acute
More Information
In triangle JKL, with angle J being acute (less than 90 degrees), angles K and L can either be both acute or one being obtuse and the other acute. This is rooted in the triangle inequality theorem that states the sum of the angles in a triangle must be 180 degrees.
Tips
- Assuming both angles must be right or obtuse: Remember that if one angle is acute, it limits the other angles accordingly, meaning at least one other angle must also be acute.
- Confusing angle relationships: Keep in mind the sum of angles should always be 180 degrees in a triangle and use this to determine the values correctly.
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