Does every right-angled triangle
contain a pair of complementary angles?
Let’s start by thinking about what
a right-angled triangle or right triangle will look like. No matter the shape or size of the
right triangle, we know that it would always have a right angle.
Next, we need to remember what
complementary angles are. These are a pair of angles that add
up to 90 degrees. So in the right triangles, do we
have a pair of angles which add to 90 degrees? We know that one of the angles in
the triangle is 90 degrees. But what about the other two?
We can remember that the angles in
a triangle add up to 180 degrees. So if we take the other two angles
and add them together, we must get 90 degrees because our right angle of 90 degrees
plus the other two angles of 90 degrees would give us 180 degrees, which would be
the sum of the three angles. Therefore, two of the angles or a
pair of angles must be complementary. So we can give our answer to the
question as yes, every right-angled triangle does contain a pair of complementary