𝐴𝐵 is a straight line. Find the value of 𝑥.
Looking at the diagram, we can see that we have this straight line 𝐴𝐵 and then three angles that sit together on this straight line. We’re asked to find the value of 𝑥, which is used in expressions for two of the angles.
The key fact that we need to use to answer this question is that angles on a straight line sum to 180 degrees. We have expressions for two of the angles in terms of 𝑥. They’re six 𝑥 degrees and nine 𝑥 degrees. And the third angle has been labelled using a little square, which means it’s a right angle, 90 degrees.
We can, therefore, form an equation, using the fact that these three angles must sum to 180 degrees. Six 𝑥 degrees plus 90 degrees plus nine 𝑥 degrees is equal to 180 degrees. To find the value of 𝑥, we need to solve this equation the first step is to simplify the equation by grouping like terms. As we have six 𝑥 degrees plus nine 𝑥 degrees, this simplifies to 15𝑥 degrees. So we have 15𝑥 degrees plus 90 degrees is equal to 180 degrees.
The next step is to subtract 90 degrees from each side of the equation. And it gives 15𝑥 degrees is equal to 90 degrees. Now, we have 15𝑥 degrees. But we just want to know what 𝑥 degrees is equal to. So we need to divide both sides of the equation by 15. 90 divided by 15 is six. So we have 𝑥 degrees is equal to six degrees.
So we’ve solved the equation and found the value of 𝑥. Now both sides have a unit included with them, this degree symbol, which means that the value of 𝑥 is just the numeric or number value of the right-hand side.
So we have that the value of 𝑥 is six.