Example 3 - Find the size of an angle
Find the size of angle \(y\).
Solution
1. What do I have to do?
Read the question through twice. Highlight or underline the important pieces of information in the question.
2. What information do I need?
The question is asking for the size of angle \(y\).
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 An angle that measures between 90掳 and 180掳., it might not be.
Write any angles onto the diagram.
3. What information don鈥檛 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掳 to create an equation.
\(4x + 29 + 5x + 11 + 2x - 3 = 180\)
Step B
Simplify the equation:
\(11x + 37 = 180\)
Step C
Solve the equation to find the value of \(x\).
\(11x + 37 = 180\)
Subtract 37 from both sides:
\(11x =143\)
Divide both sides by 11:
\(x =13\)
Step D
Use the answer to step C to work out the value of the angle highlighted.
\(x = 13\) so substitute 13 into the expression \(2x - 3\).
\(2 \times 13 - 3 = 23\)
Therefore the value of the highlighted angle is 23掳.
Step E
Use the fact that angles on a straight line add up to 180掳 to work out the value of \(y\).
\(180 - 23 = 157^\circ\)
Therefore the value of \(y\) is 157掳.
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:
\(5x + 11 = 5 \times 13 + 11 = 76^\circ\)
\(4x + 29 = 4 \times 13 + 29 = 81^\circ\)
Add these two angles to 23掳 and it should equal 180掳.
\(76^\circ + 81^\circ + 23^\circ = 180^\circ\)
6. Have I completed everything?
The answer should be the size of an angle.
Make sure the answer has the units (degrees) on it.
Nothing else was asked for.