Download SAT ACT The Exterior Angle Theorem

SAT / ACT GEOMETRY
Triangle
The Exterior Angle Theorem
An exterior angle of a triangle is equal to the sum
of the two interior angles remote from it.
Example 1 Find the measure of the exterior angle.
Solution By Exterior Angle Theorem, find z:
z = 50° + 84° = 134°.
Example 2 Find the measure of the exterior angle labeled x for the
isosceles triangle.
Solution
1). From ∆EFG find the values of angles ∠F and ∠E.
m (∠F) = m (∠E) =
180° − 118°
2
= 31°.
2) By Exterior Angle Theorem find x = m (∠HEF).
x = m (∠F) + m (∠D) = 31° + 118° = 149°
Example 3 Find the measure of ∠X.
Solution
1) ∆VUW is an isosceles triangle, therefore m (∠VWU) = m (∠V) = 50°.
2) ∆XWU is an isosceles triangle, therefore m (∠WUX) = m (∠X).
3) ∠VWU is an exterior angle of the triangle XWU and is equal to the
sum of the measures of the two remote interior angles:
m (∠VWU) = m (∠WUX) + m (∠X) ⇒ 50° = 2m (∠X)
⇒ m (∠X) = 25°
Example 4 In the figure below, find the measure of x.
Solution
m (∠ EDF) = 50°, and m (∠ DFE) = 180° − 110° =70°.
Angle x is an exterior angle of the triangle DEF and is equal to the sum
of the measures of the two remote interior angles:
x= 50º + 70º = 120º