### Video Transcript

In the displayed model of a house,
what angle does the roof make with the horizontal, given that triangle π΄πΈπ΅ is
isosceles?

Itβs probably most useful to begin
this question by highlighting the triangle π΄πΈπ΅ that we want to consider. This triangle forms the roof of
this house, and weβre told that itβs isosceles. We should recall that in an
isosceles triangle, we have two sides equal in length and two base angles are
equal. So in this diagram, the side π΄πΈ
is equal to the side π΄π΅ and the angle π΄πΈπ΅ is equal to the angle π΄π΅πΈ.

Now that weβve had a look at the
diagram, letβs focus on what weβre asked, to find the angle that the roof makes with
the horizontal. That means that weβre really
looking for the angle created by the slope of the roof and the horizontal axis. Either of the two base angles would
give us the answer for this. So letβs see if we can work out one
of these angles, angle π΄π΅πΈ.

In order to do this, weβll need to
remember an important fact about the angles in a triangle. And that is that the angles in a
triangle add up to 180 degrees. This means that we can write that
angle π΅π΄πΈ plus angle π΄πΈπ΅ plus angle π΄π΅πΈ is equal to 180 degrees. Weβre given that angle π΅π΄πΈ is
107 degrees. So if we subtract 107 degrees from
both sides of this equation, we get that angle π΄πΈπ΅ plus angle π΄π΅πΈ is equal to
73 degrees. As we have an isosceles triangle,
we know that our two base angles are equal. So angle π΄πΈπ΅ is equal to angle
π΄π΅πΈ.

We could think of this then that
two times angle π΄π΅πΈ is 73 degrees. And so to find angle π΄π΅πΈ, we
must divide both sides of this equation by two, which means that the measure of
angle π΄π΅πΈ is 36.5 degrees as a decimal. We can therefore give our answer
that the angle that the roof makes with the horizontal is 36.5 degrees.