mind your decisions i'm presh tallwalker
three squares are placed in a row
connect the bottom left corner of each
square to the top right corner of the
third square
these form three angles with the
horizontal that we will label
as a b and c
the question is what is a plus b plus c
equal to pause the video if you'd like
to give this problem a try
and when you're ready keep watching to
learn how to solve this problem
[Music]
to get started focus on angle c
the diagonal of a square is an angle
bisector
so c is equal to 45 degrees
now let's focus on angle b
the trick in this problem is to think
outside the box
we will make a mirror image copy of
these three squares
right above them consider this right
triangle
and let's consider its mirror image copy
because we have a mirror image this
angle is equal to b
now let's make one more copy of this
right triangle
let's label the two acute angles in this
triangle
one angle is equal to b so the other
angle will be equal to 90 minus b
now let's calculate the value of this
angle
because these three angles make a
straight line their sum
will be equal to 180 degrees so this
angle
is equal to 180 degrees minus the other
two angles
one angle is 90 minus b and the other
angle is equal to b
the b terms will cancel and then we have
180 minus 90
which is equal to 90. so this angle is
equal to 90 degrees
and it's a right angle
now let's go back and label angle a
notice that this side is exactly equal
to this side
because each of them is the hypotenuse
of a congruent right triangle
so these two sides are equal to each
other
now here we have a right angle triangle
where its two legs are congruent
so the other two angles in this triangle
will be equal to 45 degrees
but recall that angle c is exactly equal
to 45 degrees
so each of these angles is also equal to
c
now we can solve the problem we'll focus
on the original three squares
look at this angle it's an angle of the
square
so it's equal to 90 degrees but it's
also equal to a plus b
plus c thus we have a plus b plus c
is equal to 90 degrees and that's the
answer
what an interesting geometry problem
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see you next episode of mind your
decisions where we solve the world's
problems
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