Study Guide: Acute Angles

Definition:

An acute angle is an angle that measures greater than 0 degrees and less than 90 degrees.

Examples:

An angle measuring 30 degrees is an acute angle.
An angle measuring 60 degrees is an acute angle.
An angle measuring 89 degrees is also an acute angle.

Visualization:

To visualize an acute angle, imagine a clock. The space between the minute hand and the hour hand when the time is between 12:00 and 3:00 forms an acute angle.

Properties:

Acute angles are always less than 90 degrees.
The sum of two acute angles is always less than 180 degrees.
In a right-angled triangle, the two non-right angles are acute angles.

Practice Problems:

1. Find the measure of the acute angle in the following diagram:

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Answer: The acute angle measures 45 degrees.

2. If angle A measures 30 degrees and angle B measures 55 degrees, are they both acute angles?

Answer: Yes, both angles A and B are acute angles as they are less than 90 degrees.

◂Math Worksheets and Study Guides Sixth Grade. Mixed Numbers

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.