#5.1 Angles of Triangles

Front

What is the sum of the angles in a triangle?

Back

The sum of the angles in a triangle is always 180 degrees.

Front

Define an acute angle.

Back

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

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring exactly 90 degrees.

Front

What is the relationship between the slopes of two lines that are perpendicular?

Back

The slopes of two perpendicular lines are opposite reciprocals of each other.

Front

If one angle of a right triangle is 30 degrees, what is the measure of the other acute angle?

Back

The other acute angle measures 60 degrees, since the sum of the angles in a triangle is 180 degrees.

Front

What is the formula to find the measure of an unknown angle in a triangle?

Back

To find an unknown angle, use the formula: Unknown angle = 180 - (sum of the other two angles).

Front

How do you find the measure of an angle if you know the slopes of the sides forming that angle?

Back

You can find the angle using the formula: angle = arctan(m1) - arctan(m2), where m1 and m2 are the slopes of the sides.

Front

What is the measure of each angle in an equilateral triangle?

Back

Each angle in an equilateral triangle measures 60 degrees.

Front

If the measure of one acute angle in a right triangle is 12 more than 3 times the other acute angle, how do you express this relationship mathematically?

Back

Let x be the measure of the smaller acute angle. Then the other angle can be expressed as 3x + 12.

Front

What is the definition of complementary angles?

Back

Complementary angles are two angles whose measures add up to 90 degrees.