Question

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

Answer 1

Answer:

Step-by-step explanation:

First, alternate interior and alternate exterior angles and  corresponding require a transversal through two parallel lines.  or in other words two parallel lines with a non parallel line going through the both of them.  We don't have that here so none of those count here.  

Step 2 is the only one that mentions them so that's wrong.  The two options regarding step 2, one mentions alternate exterior angles, so that's incorrect, which means the last option is the right answer.

To logic it out let's go choice by choice.

Measure of three angles of a triangle is 180, so that's correct

Alternate interior angles are the same, so saying the difference of two angles equals 90 degrees doesn't make sense with alternate interior angles.  Also, the relationship is untrue.  So doubly wrong.

the sum of the three angles of a triangle equals 180 and the sum of two angles that when put together make a straight lineis also 180, so this is right, just with the wrong step beforehand.

Fourth step is just right.

So definitely see step 2 is the problem.  So let's look at the two replacement options.

First choice for step two says angle o + angle p does equal 180 degrees, which is true, but they are not alternate exterior angles.  So only half as wrong.  If you don't understand how they look you should do a quick search for alternate angles and see what alternate exterior and interior angles look like.  And corresponding angles.

Second choice for step 2 gets the 180 degrees right AND givs the reason that they are supplementary angles.  The definition of supplementary angles is that they add up to 180, or make a straight line, so also true.

Also we should check and make sure step 3 follows and makes sense.  Basically it says these three angles equal 180 and these two angles equal 180 so these two angles must equal these three angles, which makes sense since they equal the same number.  So check.

Let me know if Something I said didn't make sense.  Also here is a small guide of angles for the picture I uploaded with this.

Angles A and G are Alternate Exterior

D and F are Alternate Exterior

B and H are Alternate INTERIOR

E and C are Alternate Interior

A and E are Corresponding

B and F are corresponding

C and G are corresponding

D and H are corresponding

In all of these relationships it means the two angles are equal, and they require a transversal.  Let me know if you need further explanation let me know.