# Solving triangles. How to work out the angles in a triangle when the angles given are in algebra.

If the angles in a triangle are given as algebra (usually in terms of x), and you are asked to find out the size of each angle, then you can follow these 3 simple steps to find all of the angles.

**Step 1**

Add up the 3 angles that are given and simplify the expression.

**Step 2**

Turn the expression from step 1 into an equation by making it equal to 180⁰ (since the angles in a triangle add up to 180⁰. Once this is done, you can solve the equation to find the value of x.

**Step 3**

Once x is found, the size of each angle can be calculated by substituting x back into each angle.

**Example 1**

Work out the size of each angle in this triangle.

**Step 1**

Add up the 3 angles that are given and simplify the expression.

6x + 4x + 2x = 12x

**Step 2**

Turn the expression from step 1 into an equation by making it equal to 180⁰ (since the angles in a triangle add up to 180⁰. Once this is done, you can solve the equation to find the value of x.

12x = 180

x = 180 ÷ 12

x = 15⁰

**Step 3**

Once x is found, the size of each angle can be calculated by substituting x back into each angle.

Starting with the smallest angle first you get:

2x = 2 × 15 = 30⁰

4x = 4 × 15 = 60⁰

6x = 6 × 15 = 90⁰

Let’s take a look at a harder example.

**Example 2**

Work out the size of each angle in this triangle.

**Step 1**

Add up the 3 angles that are given and simplify the expression.

x + 10 + 2x + 20 + 2x – 5

= 5x + 25

**Step 2**

Turn the expression from step 1 into an equation by making it equal to 180⁰ (since the angles in a triangle add up to 180⁰. Once this is done, you can solve the equation to find the value of x.

5x + 25 = 180

5x = 180 – 25

5x = 155

x = 155 ÷ 5

x = 31⁰

**Step 3**

Once x is found, the size of each angle can be calculated by substituting x back into each angle.

Starting with the smallest angle first you get:

x + 10 = 31 + 10 = 41⁰

2x - 5 = 2 × 31 – 5 = 57⁰

2x + 20 = 2 × 31 + 20 = 82⁰

## More by this Author

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

No comments yet.