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Geometry Notes T - 4: Exterior Angle Theorem
Definition: An exterior angle of a polygon is an angle outside the polygon formed by extending one side.
b
c
a
Theorem: The measure of an exterior angle of a triangle is equal to
Corollary: The measure of an exterior angle of a triangle is
Ex: Find the value of x in each diagram:
a.
x
30
3x
b.
80
x
c.
x
3x – 25
Geometry HW: Triangles - 4
1. In each diagram, find the number of degrees in the value of x.
a.
b.
20
40
x
c.
x
d.
(140 – x)
40
x
(2x + 20)
70
x
(2x)
2. Triangle PQR is a right triangle with its right angle at R. An exterior angle at P measures 125. What is
the measure of the smallest interior angle of PQR?
3. In ABC, mB is four times as large as mA. An exterior angle at C measures 125. Find the measure
of A.
4. In DEF, mD = 2x + 4, mE = 6x – 58 and the degree measure of an exterior angle at F is represented by
5x. What kind of triangle is this and why?
5. a. Draw a diagram of triangle ABC and extend each side so that there is one exterior angle at each vertex.
b. If mA = a, represent the measure of an exterior angle at A in terms of a. Using b and c for the
measures of the interior angles, find expressions for the exterior angles at B and C.
c. Find the sum of the measures of the exterior angles of a triangle (one exterior angle at each vertex) in
simplest form.
l1
x
6. In the diagram at right, l1 || l2, mx = 120 and my = 135, find mz.
z
y
l2
60 40
7. Find the values of x, y and z in the diagram at right.
50
x y
z
8. Find the values of x, y and z in the diagram at right.
y
65
x
9. Triangle ABC has vertices at A(–2, 3), B(4, 7) and C(6, –1).
a. Find the coordinates of M, the midpoint of AB , and N, the midpoint of BC .
b. Show using coordinate geometry that MN || AC .
c. What is the relationship between the measures of BAC and BMN?
d. What is the relationship between the measures of ACB and MNC?
e. Given that mACB = 49.40 and mNMB = 60.26, find mABC.
60
z
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