# Triangles for SQA National 5 Maths 1. Sum of angles in a triangle
2. Pythagoras' theorem

The sum of the angles in any triangle is 180º. This property can be used to calculate missing angles in triangles. The hypotenuse of a right-angled triangle is its longest side and is always opposite the right angle. The square of the hypotenuse can be found by adding the squares of the other two sides of the triangle. # 1

State the sum of the angles in a triangle.

The sum of the angles in any triangle is 180º. # 2

Use the given diagram to calculate the value of x.

Using Pythagoras' Theorem, x² + (3x)² = 10², so 10x² = 100 and x² = 10 and x = √10. # 3

Find the value of x in the given triangle.

The angle next to the 100º angle is given by 180 − 100 = 80º.
The second angle in the triangle is alternate angles with the 50º angle, therefore is equal to 50º.
So, x = 180 − (80 + 50) = 50º. # 4

Calculate the value of x.

Using Pythagoras' Theorem, x² + 20² = 25², so x² = 225 and x = 15. # 5

Use the given triangle to show that the angles in a triangle add up to 180º.

The angles vertically opposite the two 60º angles are also 60º.
The angle next to the 120º angle is 180 − 120 = 60º.
So, sum of angles = 60 + 60 + 60 = 180º. End of page