The angles in a triangle are in the ratio 1 : 2 : 3 - OCR - GCSE Maths - Question 8 - 2017 - Paper 1

To show that the triangle is a right-angled triangle, we can start by expressing the angles of the triangle based on the given ratio of 1:2:3. Let the common multiplier be represented as $x$. Thus, the angles can be expressed as:

• First angle: $1x = x$
• Second angle: $2x = 2x$
• Third angle: $3x = 3x$

Now, according to the triangle sum property, the sum of angles in a triangle is $180^{ ext{o}}$. Therefore:

$x + 2x + 3x = 180^{ ext{o}}$

This simplifies to:

$6x = 180^{ ext{o}}$ $x = 30^{ ext{o}}$

Thus the angles of the triangle are:

• First angle: $30^{ ext{o}}$
• Second angle: $60^{ ext{o}}$
• Third angle: $90^{ ext{o}}$

Since one angle is $90^{ ext{o}}$, we conclude that this triangle is indeed a right-angled triangle.