A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC b
elow 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 p. The angle adjacent to w is marked as o, and the other two angles inside the triangle are marked as m and n
. Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle) Step 2: m∠p − m∠o = 90 degrees (alternate interior angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
First you must take into account the variable that is being defined for this case: c = represents the number of puppies whose eyes are closed. We can then write the following equation: 15 = 11 + c Rewriting the equation: 11 + c = 15 Clearing c: c = 15-11 c = 4 4 puppies have their eyes closed Answer: 11 + c = 15 4 puppies have their eyes closed