### Video Transcript

π΄π΅πΆ is an isosceles triangle. Line π΄π΅π· is a straight line. Determine whether triangle π΄π΅πΆ is a right-angled triangle or not. You must give a reason for each step of your working.

Now because π΄π΅πΆ is an isosceles triangle, we know that two of the sides are equal in length. And we sometimes use the word congruent to describe that and their opposite angles sometimes known as the base angles of the isosceles triangle are also equal. And weβre also told that line π΄π΅π· is a straight line.

So how weβre gonna use this information to determine whether triangle π΄π΅πΆ is a right-angled triangle? Well, letβs start with the fact that line π΄π΅π· is a straight line. Well, we know that angles on a straight line sum to 180 degrees. And this means that angle π΄π΅πΆ plus angle πΆπ΅π· must equal 180 degrees. And we know that angle πΆπ΅π· is 133 degrees. So angle π΄π΅πΆ plus 133 degrees is 180 degrees. And subtracting 133 degrees from each side of that equation tells us that angle π΄π΅πΆ is 47 degrees.

So letβs mark that on our triangle. Now, we know that base angles in an isosceles triangle are equal. So that means that angle π΄πΆπ΅ is equal to angle π΄π΅πΆ. And we know that angle π΄π΅πΆ is 47 degrees. So that tells us that angle π΄πΆπ΅ is also 47 degrees. And lastly, we know that angles in a triangle add up to 180 degrees. So angle π΅π΄πΆ plus angle π΄π΅πΆ plus angle π΄πΆπ΅ is 180 degrees.

And we just worked out that angles π΄π΅πΆ and π΄πΆπ΅ are both 47 degrees. So if we take 47 degrees away from both sides of the equation twice, weβve got angle π΅π΄πΆ is equal to 180 degrees minus 47 degrees minus another 47 degrees. Now, that means that angle π΅π΄πΆ is 86 degrees.

So the three angles in triangle π΄π΅πΆ are 86 degrees, 47 degrees, and 47 degrees. And since none of the angles in the triangle are 90 degrees, itβs not a right-angled triangle.