(02.07)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 p. The angle adjacent to p 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)
Question 2(Multiple Choice Worth 4 points)
(02.07)The figure shows two parallel lines AB and DE cut by the transversals AE and BD:

AB and DE are parallel lines and AE and BD are transversals. The transversals intersect at C. Angle CAB is labeled 1, angle ABC is labeled 2, angle ACB is labeled 3, angle ACE is labeled 4, angle CDE is labeled 6, and angle CED is labeled 5.

Which statement best explains the relationship between Triangle ABC and Triangle EDC ?

Triangle, because m∠3 = m∠6 and m∠1 = m∠4
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
Triangle ABC is similar to triangle EDC , because m∠6 = m∠2 and m∠3 = m∠4
Question 3(Multiple Choice Worth 4 points)
(02.07)The image shown has two triangles sharing a vertex:

There are two triangles labeled RST and TUV with a common vertex T. In triangle RST, angle SRT is labeled as y, and angle RST is labeled as 55 degrees. In triangle TUV, angle TUV is labeled as 55 degrees.

What is the measure of ∠TVU, and why?

y, because Triangle RST is similar to triangle VUT
y over 2, because Triangle RST is congruent to triangle VUT
y + 55 degrees, because Triangle RST is similar to triangle TUV
125 degrees − y, because Triangle RST is congruent to triangle TUV
Question 4(Multiple Choice Worth 4 points)
(02.07)Two similar triangles are shown below:

Two triangles are shown. The sides of the triangle on the left are marked 6, 4, 3. The sides of the triangle on the right are marked as 3, 2 and 1.5. For the triangle on the left, the angle between sides marked 4 and 6 is labeled as w, marked by a double arc, and the angle between the sides marked 6 and 3 is labeled as x, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 3 and 1.5 is labeled as y and the angle between the sides marked 2 and 3 is labeled as v, marked by a double arc. The angle between the sides 2 and 1.5 is labeled as z, marked by a triple arc, and it is also the angle on the top vertex of this triangle.

Which two sets of angles are corresponding angles?

∠w and ∠v; ∠x and ∠y
∠w and ∠y; ∠x and ∠v
∠w and ∠z; ∠x and ∠v
∠w and ∠z; ∠x and ∠y
Question 5(Multiple Choice Worth 4 points)
(02.07)Which relationship is always true for the angles x, y, and z of triangle MNP?

A triangle is shown with a leg extending past the top vertex. The vertices are labeled MNP. Angle y is located inside the triangle at vertex N. Angle z is located inside the triangle at vertex P. Angle x is located inside the triangle at vertex M.

x + z = y
y + z = x
x + y + z = 180 degrees
x + y + z = 90 degrees