Calculate the size of angle 𝑥.
There are few things to be aware of before we start this question. Firstly, it says that the diagram is not drawn accurately. This means that we can’t measure the angle with a protractor. We have to use our angle properties. It is also important to note that the line marked in orange appears to be a straight line. However, we cannot assume this, unless we’ve been told it is definitely a straight line. In this case, it is not. This means that we can’t use the angle property that angles on a straight line add up to 180 degrees.
The angle marked with a square or box is a right angle and is therefore equal to 90 degrees. The angle property that we will use to solve this question is that angles in a circle or at a point sum or add up to 360 degrees. The five angles inside the circle must add up to 360. We can write this as an equation: 𝑥 plus 102 plus 50 plus 90 plus 42 is equal to 360. Our first step is to simplify the equation by adding 102, 50, 90, and 42. These four numbers sum to 284. Therefore, 𝑥 plus 284 is equal to 360.
Our final step to calculate the value of 𝑥 is to subtract 284 from both sides of the equation. 284 minus 284 is equal to zero. Therefore, we have 𝑥 on the left-hand side. 360 minus 284 is equal to 76. This means that the size of angle 𝑥 is 76 degrees. We can substitute this value back into our initial equation to check that our answer is correct. 76 plus 102 plus 50 plus 90 plus 42 is indeed equal to 360.