### Video Transcript

Given that triangle π
ππ is congruent to triangle πππ, find the values of π₯ and π¦.

When weβre given a congruency relationship between two triangles, we can use the order of the letters to help us identify congruent angles. If we take angle π
in triangle π
ππ, we could see that this is congruent to angle π in triangle πππ. Angle π in triangle π
ππ, or more specifically angle π
ππ, is congruent with angle π in triangle πππ. Our final third angle in each triangle, angle π in triangle π
ππ and angle π in triangle πππ, are also congruent.

So to find the angle π₯, we know that this equates to angle π. This will be congruent to angle π
in triangle π
ππ. We donβt know the value of angle π
. But we can work it out using a key fact about the angles in a triangle. And that is that the angles in a triangle add up to 180 degrees.

And therefore, to find angle π
in triangle π
ππ, we have 180 degrees subtract 29 degrees and subtract 90 degrees, which gives us 61 degrees. So now we know that angle π
is 61 degrees. And therefore, the congruent angle π must also be 61 degrees. So π₯ must be equal to 61. Notice that we donβt need to include the degree symbol since it was already given to us.

We could also have solved for π₯ by recognising that angle π is also 29 degrees since itβs congruent to angle π in triangle π
ππ. And then calculate it using the angle sum in our triangle. To find the value of π¦, for the next part of the question, we need to look at the congruent sides in our triangles. We know that since the line ππ is in both triangles, then this is a congruent side in each triangle. The line π
π in triangle π
ππ is congruent to the line ππ in triangle πππ. We could also see this from the pattern in the letters in each triangle.

And finally, we can say that line π
π in triangle π
ππ is congruent to line ππ in triangle πππ. Since weβre told that the line ππ is 42 and the line π
π is two π¦ minus four, then we can set these equal and solve for π¦. We have two π¦ minus four equals 42. So rearranging by adding four will give us two π¦ equals 42 plus four, which is 46. We then divide both sides of the equation by two, to give π¦ equals 23. Therefore, our final answer is π₯ equals 61, π¦ equals 23.