Question

100 POINTS

In the graphic below, exterior angle
In your own words using the graphic and variables included, is the
following statement always true?

The measure of an exterior angle of a triangle is equal to the
sum of the measures of its remote interior angles.

Be sure to explain using mathematical language and vocabulary from
this Geometry course. Show an example using numbers to illustrate
this theorem.

Answer 1

Answer:

• Yes

Step-by-step explanation:

In the given diagram we have:

• exterior angle is d
• remote interior angles are b and c
• adjacent angle is a

The following equation is true:

• d = b + c

It makes the statement true and it can be proven by the sum of interior angles.

• a + b + c = 180        sum of interior angles is 180°
• a + d = 180              linear pair is 180°
• a + b + c = a + d      substitution
• b + c = d                  cancel a on both sides