### Video Transcript

π΄π΅ is a straight line. Find the value of π₯.

Looking at the diagram, we can see that we have this straight line π΄π΅ and then three angles that sit together on this straight line. Weβre asked to find the value of π₯, 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 π₯. Theyβre six π₯ degrees and nine π₯ degrees. And the third angle has been labelled using a little square, which means itβs a right angle, 90 degrees.

We can, therefore, form an equation, using the fact that these three angles must sum to 180 degrees. Six π₯ degrees plus 90 degrees plus nine π₯ degrees is equal to 180 degrees. To find the value of π₯, we need to solve this equation the first step is to simplify the equation by grouping like terms. As we have six π₯ degrees plus nine π₯ degrees, this simplifies to 15π₯ degrees. So we have 15π₯ 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 15π₯ degrees is equal to 90 degrees. Now, we have 15π₯ degrees. But we just want to know what π₯ 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 π₯ degrees is equal to six degrees.

So weβve solved the equation and found the value of π₯. Now both sides have a unit included with them, this degree symbol, which means that the value of π₯ is just the numeric or number value of the right-hand side.

So we have that the value of π₯ is six.