| Lesson
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Math
A |
Exterior
Angles
of a Triangle |
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An
exterior angle of a triangle is equal in measure to the sum of
the two non-adjacent interior angles of the triangle |
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In
the triangle to the right, <4 is an exterior angle, because
it is formed by a side of the triangle and an extension of
another side. |
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The
theorem above states that because <4 is an exterior angle,
its measure is equal to the sum of the measures of the 2
interior angles to which it is not adjacent,
namely, <2 and <3. |
| 1. |
In
 PQR,
m<Q = 45º, and m<R = 72º. Find
the measure of an exterior angle at P. |
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It
is always helpful to draw a diagram and label it with the given
information. |
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Then,
using the theorem above, set the exterior angle ( x ) equal to
the sum of the two non-adjacent interior angles
(45º and 72º.) |
x
= 45 + 72
x = 117
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So,
an exterior angle at P measures 117º. |
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| 2. |
In
DEF, an
exterior angle at F is
represented by 8x + 15. If the two
non-adjacent interior angles are represented
by 4x + 5,
and 3x + 20, find the value of x. |
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First,
draw and label a diagram.
Next,
use the theorem to set up an equation.
Then
solve the equation for x. |
8x+15=(4x+5)+(3x+20)
8x+15 = 7x + 25
8x = 7x + 10
x = 10
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| 3. |
Find
the measure of an exterior angle at the base of an isosceles triangle whose
vertex angle measures 40º. |
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First.....the
diagram.
You may choose either of the
exterior angles at B or C. They will
have the same measure.
Next,
we have to find the measure of a base angle----let's say <B.
Remember
that the 2 base angles of an isosceles triangle are equal, so we'll represent each as y.
Then,
write an equation, using the theorem from the previous lesson.
Now we
can solve for x using the theorem above. Set the exterior
angle equal to the two non-adjacent interior angles.
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y + y
+ 40 = 180
2y + 40 = 180
2y = 140
y = 70
x = 70
+ 40
x = 110
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So,
an exterior angle at the base measures
110º. |
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