Angles in Triangles and Quadrilaterals

Question 1

What do angles around a point add up to?

Answer 1

360°

Question 2

What do angles on a straight line add up to?

Answer 2

180°

Question 3

When to straight lines intersect, what is the rule for the angles and how does one prove it?

Answer 3

The opposite angles are equal, because the angles on each straight line have to add together to make 180°.

Question 4

One parallel lines, what is the rule?

Answer 4

A straight line passing through two parallel lines will form the same angle against each of the lines.

Question 5

What do the interior angles of a triangle add up to?

Answer 5

They add up to 180°, which can be proved by drawing a line parallel to the base as the top of the tringle.

Question 6

What are interior and exterior angles?

Answer 6

An interior angle is simply the angle on the inside, and the exterior angle and is the angle formed if you continue one of the lines along. E = 180° - I.

Question 7

In a triangle, what does the exterior angle equal?

Answer 7

The sum of the other two interior angles.

Question 8

How do you classify quadrilaterals?

Answer 8

Square - 4 equal sides and four 90° angles
Rectangle - four 90° angles
Rhombus - 4 equal sides
Parallelogram - Two pairs of parallel sides
Kite - Two pairs of equal sides. Corners bisect at right angles
Dart - Two pairs of equal sides. One reflex angle
Trapezium - One pair of Parallel sides

Question 9

What do the internal angles in a quadrilateral add up to?

Answer 9

They add up to 360° because every quadrilateral can be split into two triangles, each with angles adding up to 180°.

Question 10

What is the formula for the sum of the interior angles in an n-gon.

Answer 10

180°(n - 2)

Question 11

What is the formula for an interior angle in a regular n - gon?

Answer 11

[180°(n - 2)] / n

Question 12

What is the sum of the exterior angles on a polygon?

Answer 12

180°n - [180°(n - 2)]
= 180°n - 180° + 360°
=360°