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

Questions & Answers

Question: How would I solve this? In a right angle triangle, one of the acute angles is 40 greater than the other. Find the angles of triangle.

Answer: The three angles in the triangle are x, x + 40 and 90.

Adding these up gives 2x + 130.

Make 2x + 130 = 180.

2x = 50

x =25.

So substituting x = 25 will give 90, 25 and 65.

Question: What if the angles of the triangle were as follows: x+10, x+20 and the third missing angle was unknown, represented by w. Knowing that all interior angles of a triangle equal 180 degrees, how would you solve for w?

Answer: You will have to express w in terms of x.

Adding up the two angles gives 2x + 30.

Subtract this from 180 gives 150 -2x.

So w = 150 - 2x.