In order to find 𝑥, we’re actually gonna have to find another angle first. And the first angle that we’re gonna look at is angle 𝐴𝐵𝐶. And I’ve marked this angle on our diagram in orange. And angle 𝐴𝐵𝐶 is gonna be equal to 180 degrees minus 84 degrees, which is equal to 96 degrees.
So we’ve actually found out what angle 𝐴𝐵𝐶 is. However, in these types of questions, what you always need to do is you actually need to give reasoning for what you’ve done. So the reason for our answer is that as angles on a straight line are equal to 180 degrees.
And you can see that angle 𝐴𝐵𝐶 and angle 𝐶𝐵𝐷 both put together form a straight line. So it would form a 180 degrees. Okay, great! Now let’s move on and find 𝑥.
Well the next thing we know is that angle 𝐴𝐶𝐵 is equal to angle 𝐵𝐴𝐶. So therefore, they’re both 𝑥. And we know that these angles are equal because they’re angles in an isosceles triangle, and they’re the two base angles.
And we know that because actually as I’ve marked in pink, we have these two lines which show us that side 𝐴𝐵 is equal to side 𝐵𝐶. Okay, great! so they’re both equal to 𝑥. So now let’s find 𝑥. So therefore, we can say that two 𝑥 is going to be equal to a 180 degrees minus 96 degrees.
So two 𝑥 is gonna be equal to 84 degrees. So that’s angle 𝐴𝐶𝐵 plus angle 𝐵𝐴𝐶 is equal to 84 degrees. And we know that because our angles in a triangle equals 180 degrees. So that would be 𝑥 plus 𝑥 plus 96 would equal 180 degrees.
Okay, great! So now let’s find 𝑥. So therefore, if we divide 84 and two 𝑥 by two, we get 𝑥 is equal to 42. And this is our final answer. So just a quick reminder, whenever you’re doing in this type of problem, do remember at each step to include your reasoning.
So for instance, as we did in the first part, we said that angle 𝐴𝐵𝐶 was equal to 180 minus 84 which equals 96 degrees and that was because angles on a straight line equal 180.