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.

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The resources above cover the following skills:

NUMBER SENSE

Know commonly used fractions (halves, thirds, fourths, fifths, eighths, tenths) and their decimal and percent equivalents. Convert between any two representations (fractions, decimals, percents) of positive rational numbers without the use of a calculator.