Canada Grade 6 Math Measuring angles

What is the measure of a right angle?

• 45 degrees

• 90 degrees

• 180 degrees

• 360 degrees

Answer explanation

A right angle is defined as an angle that measures exactly 90 degrees. This is a fundamental concept in geometry, distinguishing it from other angles like acute (less than 90 degrees) and obtuse (greater than 90 degrees).

• 60 degrees

• 90 degrees

• 120 degrees

• 150 degrees

Answer explanation

In a triangle, the sum of angles is 180 degrees. Given angles A (30 degrees) and B (60 degrees), we can find angle C by calculating 180 - (30 + 60) = 90 degrees. Therefore, angle C measures 90 degrees.

What is the measure of an angle that is supplementary to a 110-degree angle?

• 70 degrees

• 80 degrees

• 90 degrees

• 100 degrees

Answer explanation

To find the angle supplementary to a 110-degree angle, subtract 110 from 180. Thus, 180 - 110 = 70 degrees. Therefore, the angle that is supplementary to a 110-degree angle is 70 degrees.

Which of the following angles is an acute angle?

• 95 degrees

• 90 degrees

• 85 degrees

• 180 degrees

Answer explanation

An acute angle is defined as an angle less than 90 degrees. Among the options, 85 degrees is the only angle that meets this criterion, making it the correct choice. The other angles are either right or obtuse.

What is the measure of an angle that is complementary to a 25-degree angle?

• 55 degrees

• 65 degrees

• 75 degrees

• 85 degrees

Answer explanation

To find the complementary angle, subtract the given angle from 90 degrees. So, 90 - 25 = 65 degrees. Therefore, the angle that is complementary to a 25-degree angle is 65 degrees.

If two angles are vertical angles and one measures 45 degrees, what is the measure of the other angle?

• 45 degrees

• 90 degrees

• 135 degrees

• 180 degrees

Answer explanation

Vertical angles are equal. Since one angle measures 45 degrees, the other angle also measures 45 degrees.

What is the measure of an angle that forms a straight line with a 130-degree angle?

• 50 degrees

• 60 degrees

• 70 degrees

• 80 degrees

Answer explanation

The angles on a straight line sum to 180 degrees. Therefore, if one angle is 130 degrees, the other angle is 180 - 130 = 50 degrees. Thus, the measure of the angle that forms a straight line with a 130-degree angle is 50 degrees.

Which of the following is a reflex angle?

• 45 degrees

• 90 degrees

• 135 degrees

• 270 degrees

Answer explanation

A reflex angle is greater than 180 degrees and less than 360 degrees. Among the options, 270 degrees fits this definition, making it the correct choice. The other angles (45, 90, 135 degrees) are not reflex.

• 20 degrees

• 30 degrees

• 40 degrees

• 60 degrees

Answer explanation

Let angle Y = y. Then angle X = 3y. The equation is y + 3y = 120. This simplifies to 4y = 120, so y = 30. Therefore, angle Y measures 30 degrees.

What is the measure of an angle that is 1/4 of a full rotation?

• 45 degrees

• 90 degrees

• 180 degrees

• 270 degrees

Answer explanation

A full rotation is 360 degrees. To find 1/4 of a full rotation, divide 360 by 4, which equals 90 degrees. Therefore, the measure of the angle that is 1/4 of a full rotation is 90 degrees.