Question number 12, what is the measure of the angle indicated with the question mark right over here? So what we have is two triangles that are laid on top of one another, some angles are marked and the one with the question mark here is the one we have to consider and compute its measure. So let's fill in all the missing information that we can at this point. We have here a 330 degree angle, so the missing measure to make this a full angle of 360 degrees is 30 degrees, so that's the measure of the angle right here, that's 30 degrees. Here we have a right angle, so that would be a right angle over here and a right angle over here, we have these two small right triangles and knowing that the triangle on the lower right has a 20 degree angle in there, its complement here has to be 70 degrees as the measure of the third angle like so. And then we can keep going, we know that the supplement of that 70 degree angle is the angle over here and that would be 180 degrees minus 70 degrees, so that is 110 degrees, the supplement of that angle. And so now we have a triangle here that I will trace out in red with a 30 degree angle that we have computed with a 110 degree angle that we have computed and the missing angle here indicated by the question mark. So we have that the question mark here, that angle plus 30 degrees plus 110 degrees has to be equal to 180 degrees as is well known, so the question mark measure is 180 degrees minus 110 minus 30, that gives us 70 degrees minus 30 degrees and so finally after subtracting twice we see that the missing angle here indicated by the question mark measures exactly 40 degrees and so the answer we mark here is B.

triangles

angles

supplementary

geometry

calculation