Question

Explaining Approaches to Finding Exterior Angles
Walden was given a triangle that had 3 exterior angles labeled with expressions. Lisa was given a triangle that had an exterior angle and 2 remote interior angles labeled with expressions. Can Walden and Lisa use the same approach to find the unknown angles? Explain.

Answer 1

No — they usually use different facts.

- Walden (three exterior angles labeled): use the fact that the three exterior angles of a triangle (one at each vertex) sum to 360°. If the exterior angles are given by expressions A, B, C then
A + B + C = 360,
and you solve that equation for the unknown(s).

- Lisa (one exterior and the two remote interior angles labeled): use the Exterior Angle Theorem: an exterior angle equals the sum of the two remote interior angles. If the exterior is E and the remote interiors are I1 and I2 then
E = I1 + I2,
and you solve that equation.

These are distinct approaches because Walden is using a global sum property of all three exteriors, while Lisa uses the local exterior-angle = sum-of-remote-interiors relationship. (They are related facts — if you replace each exterior by the sum of its two remote interiors and add them you recover 360° — but you would not generally solve Walden’s problem by Lisa’s single-equation method or vice versa unless the given expressions make that possible in a special case.)

Example:
- Walden: exteriors 2x, 3x+10, 4x−20 → 2x + (3x+10) + (4x−20) = 360 → 9x −10 = 360 → x = 41.111...
- Lisa: exterior 4x, remote interiors x+20 and 2x−10 → 4x = (x+20) + (2x−10) → 4x = 3x +10 → x = 10.