Canada Grade 8 Math Geometry Properties of angles, triangles

What is the sum of the interior angles of a triangle?

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

Answer explanation

The sum of the interior angles of a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry, making 180 degrees the correct answer.

Tags

CCSS.8.G.A.5

Which of the following is a property of an equilateral triangle?

• All angles are 90 degrees

• All sides are equal

• Two sides are equal

• No sides are equal

Answer explanation

An equilateral triangle has all sides equal in length, which also means all angles are equal to 60 degrees. Therefore, the correct property is 'All sides are equal', making it distinct from the other options.

Tags

CCSS.4.G.A.2

What is the measure of each interior angle in a regular hexagon?

• 90 degrees

• 108 degrees

• 120 degrees

• 135 degrees

Answer explanation

In a regular hexagon, the formula for the measure of each interior angle is (n-2) * 180° / n, where n is the number of sides. For a hexagon (n=6), each angle measures (6-2) * 180° / 6 = 120°. Thus, the correct answer is 120 degrees.

If one angle of a triangle is 90 degrees, what type of triangle is it?

• Acute triangle

• Right triangle

• Obtuse triangle

• Equilateral triangle

Answer explanation

A triangle with one angle measuring 90 degrees is classified as a right triangle. This is the defining characteristic of right triangles, distinguishing them from acute and obtuse triangles.

Tags

CCSS.4.G.A.2

What is the sum of the exterior angles of any polygon?

• 180 degrees

• 270 degrees

• 360 degrees

• 540 degrees

Answer explanation

The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides. This is a fundamental property of polygons.

In an isosceles triangle, which of the following is true?

• All sides are equal

• Two sides are equal

• No sides are equal

• All angles are different

Answer explanation

In an isosceles triangle, by definition, two sides are equal in length, while the third side can be different. Therefore, the correct choice is 'Two sides are equal'.

Tags

CCSS.2.G.A.1

What is the measure of each exterior angle in a regular pentagon?

• 60 degrees

• 72 degrees

• 90 degrees

• 108 degrees

Answer explanation

In a regular pentagon, the sum of the exterior angles is always 360 degrees. Since there are 5 angles, each exterior angle measures 360° ÷ 5 = 72°. Therefore, the correct answer is 72 degrees.

Which of the following is a property of a parallelogram?

• Opposite sides are parallel and equal

• All angles are 90 degrees

• All sides are equal

• It has no parallel sides

Answer explanation

A parallelogram has the property that opposite sides are both parallel and equal in length. The other options describe properties of different shapes, making the first choice the correct one.

Tags

CCSS.HSG.CO.C.11

What is the sum of the interior angles of a quadrilateral?

• 180 degrees

• 270 degrees

• 360 degrees

• 540 degrees

Answer explanation

The sum of the interior angles of a quadrilateral is calculated using the formula (n-2) x 180 degrees, where n is the number of sides. For a quadrilateral (4 sides), it is (4-2) x 180 = 360 degrees.

If a triangle has angles measuring 30 degrees, 60 degrees, and 90 degrees, what type of triangle is it?

• Equilateral triangle

• Isosceles triangle

• Scalene triangle

• Right triangle

Answer explanation

A triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees contains a right angle (90 degrees). Therefore, it is classified as a right triangle, which is characterized by having one angle equal to 90 degrees.

Tags

CCSS.4.G.A.2