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: 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.
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.
