In the figure, triangle 𝐷𝐵𝐶 is
symmetrical about line 𝐿. If the measure of angle 𝐶 is 69
degrees, what is the measure of angle 𝐴𝐵𝐷?
We’re told that triangle 𝐷𝐵𝐶 is
symmetrical about line 𝐿. So it’s a mirror image over this
line. We are also told that the measure
of angle 𝐶 is 69 degrees, and we want to find the measure of angle 𝐴𝐵𝐷.
It’s very important that triangle
𝐷𝐵𝐶 is symmetrical about line 𝐿, because if the measure of angle 𝐶 is 69
degrees, the measure of angle 𝐶𝐷𝐵 must also be 69 degrees. And this is because if we would
take our yellow triangle and fold it over the blue line, those angles would land on
top of each other, should they- should be the exact same 69 degrees. And this is helpful for a few
All angles of triangle 𝐷𝐵𝐶 must
add up to be 180 degrees, because a triangle always does. So we can find this last angle of
the triangle by setting 69 plus 69 plus 𝑥 equal to 180 degrees. 69 plus 69 is 138, and if we
subtract 138 from both sides of the equation, we find that 𝑥 is equal to 42
So how will this help us find the
measure of angle 𝐴𝐵𝐷? Well, the measure of angle 𝐵
completely is 90 degrees, because of that box. So if we can call our missing angle
𝑦, then that angle plus 42 should equal 90. So to solve for 𝑦, we need to
subtract 42 from both sides of the equation, resulting in that angle equaling 48
degrees. Therefore, the measure of angle
𝐴𝐵𝐷 is equal to 48 degrees.