Question

Prove theorems about triangles

Answer 1

a) It is possible and it is the only proper value of angle 2

b) Explanation Below

Angle 1 adds to the two other internal angles to get 180

(angle1) + 30 + 42 = 180

angle1 + 72 = 180

angle1 = 180-72

angle1 = 108 degrees

Subtract this from 180 to find the measure of angle 2

angle2 = 180 - angle1

angle2 = 180-108

angle2 = 72

A shortcut is to use the remote interior angle theorem to add up the interior angles 30 and 42 to get 72 as our exterior angle that is not adjacent to any of the interior angles we just added. Hence the "remote" portion.

Answer 2

a) possible
b) justification
Step 1: find value of angle 1
- you know the angles inside a triangle add up to 180 deg.
- add up the inside angles
30 + 42 + x = 180
(x=angle 1)
- x = 180-72
- x = 108
- angle 1 = 108

Step 2: Notice that angle 1 and angle 2 are supplementary (they have to add up to 180) because they are on a straight line.
- 108+x=180
(x = angle 2)
- x= 180 - 108
- x= 72 (proof complete)