Question

Guide

Leo argues that the measure of an exterior angle of a triangle is
equal to the sum of the measures of the two remote interior angles of
the triangle. He uses the diagram shown in his argument.
Xº
Leo writes the steps listed.
Step 1.r+x=180, since the sum of the measures of supplementary
angles is 180°
Step 2. p+q+r=180, since the sum of the measures of the angles
of any triangle is 180°
Which equations follow from step 1 and step 2 that Leo could use to
complete his argument?
r+x=p+q+r
r+x-r=p+q+r-r
x=p+q
p+q+r=180
bp+q+r-r=180-r
p+q=180-r
x+r=p+q+r
x+r-r=p+q+r+r
x=p+q+2r
(r+x) + (p+q+r)=180+180
2r+x+p+q=360

Answer 1

Step-by-step explanation: It looks like Leo is trying to prove that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle. From the equations given, it seems that Leo is using the fact that the sum of the measures of supplementary angles is 180 degrees, and the sum of the measures of the angles of any triangle is 180 degrees, to try to prove his statement. Some equations that Leo could use to complete his argument might include:

x = p + q, which follows from the equation r + x = 180 and the substitution of p + q + r = 180

p + q = 180 - r, which follows from the equation p + q + r = 180 and the substitution of r + x = 180

x = p + q + 2r, which follows from the equation x + r = p + q + r and the substitution of r + x = 180

It's not clear from the information given whether these equations are sufficient to prove Leo's statement, as we don't have any information about the values of p, q, r, or x. However, these equations might be a good starting point for Leo to continue his argument.