How To Solve Algebraic Problems Involving Angles In a Triangle

In a previous article, we looked at how simple algebraic problems can be solved, the case in point being a rectangle. In this example, notice how similar steps have been followed, except that instead of a perimeter of a rectangle, we shall be considering the angles in a triangle.

As before, the material has been provided by BBC Bitesize


Find the size of angle Equation: y.

1. What Do I Have To Do?

Read the question through twice. Highlight or underline the important pieces of information in the question, as done above.

2. What Information Do I Need?

The question is asking for the size of angle Equation: y. The question involves work on geometry and it may be necessary to use some angle facts.

In this diagram there is a triangle and a straight line. Although the angle looks obtuse, it might not be. Write any angles onto the diagram.

3. What Information Don’t I Need?

Everything in this question is relevant to working out the answer.

4. What Maths Can I Do?

Step A

Use the fact that the sum of the angles in a triangle are equal to 180° to create an equation.

Equation: 4x + 29 + 5x + 11 + 2x - 3 = 180

Step B

Simplify the equation:

Equation: 11x + 37 = 180

Step C

Solve the equation to find the value of Equation: x.

Equation: 11x + 37 = 180

Subtract 37 from both sides:

Equation: 11x =143

Divide both sides by 11:

Equation: x =13

Step D

Use the answer to step C to work out the value of each angle.


Equation: x = 13, so substitute 13 into the expression Equation: 2x - 3.

Equation: 2 times 13 - 3 = 23

Therefore the value of the highlighted angle is 23°.

Step E

Use the fact that angles on a straight line add up to 180° to work out the value of Equation: y.

Equation: 180 - 23 = 157^circ

Therefore the value of Equation: y is 157°.

5. Is my solution correct?

It is important to check any calculations at the end.

Go through and check them carefully.

Work out the other angles in the triangle:

Equation: 5x + 11 = 5 times 13 + 11 = 76^circ

Equation: 4x + 29 = 4 times 13 + 29 = 81^circ

Add these two angles to 23° and it should equal 180°.

Equation: 76^circ + 81^circ + 23^circ = 180^circ

6. Have I completed everything?

The answer should be the size of an angle.

Make sure the answer has the unit (degrees) on it. 

Nothing else was asked for.

And there you go, your solution all tied up in a perfect, neat, little bow.

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