A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as w. The angle adjacent to w is marked as z, and the other two angles inside the triangle are marked as x and y. Step 1: m∠x + m∠y + m∠z = 90 degrees (sum of adjacent angles) Step 2: m∠w + m∠z = 180 degrees (supplementary angles) Step 3: Therefore, m∠x + m∠y + m∠z = m∠w + m∠z Step 4: So, m∠x + m∠y = m∠w In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (sum of angles of a triangle) Step 1; it should be m∠x + m∠y + m∠z = 180 degrees (corresponding angles) Step 2; it should be m∠w + m∠z = 90 degrees (supplementary angles) Step 2; it should be m∠w + m∠z = 90 degrees (adjacent angles)
which do you think the answer is?
close, you are right in that the error was made in step 1, but the reasoning isn't quite there..
ohhh so its c
do you understand what corresponding angles are?
No, c indicates that step 2 is the one with the error..
yes i do what do you think the answe might be and ok
can you explain?
I believe it is A because see how they said in step 1 " m∠x + m∠y + m∠z = 90 degrees (sum of adjacent angles)" but when you look at the diagram, the angles indicated are actually the internal angles of the triangle..
And in geometry, the sum of the internal angles of a triangle is always 180º, so m∠x + m∠y + m∠z must = to 180, not 90, because its the sum of the interior angles of the triangle
does that make sense?
oh ok ok can you help me with a few more maybe and yes it does (: