Angles of Triangles and Quadrilaterals
10-10
The angles determined by the sides of a triangle
are called its interior angles, or simply, its angles.
If you tear off two angles of a triangle and place
the pieces next to the third angle, the angles
would form a straight angle. Thus, thesum
of the measures of the interior angles of any
triangle is 180°.
In PQRat the right, if mP55° and mQ25°, what is mR?
mPmQmR180°
55° 25° mR180°
80° mR180°
80°80° mR180°
mR100°
Simplify.
80° Subtract 80° to
Simplify. isolate mR.
Simplify.
225° Subtract 225° to
Simplify. isolate mE.
If you draw one diagonal of a quadrilateral, as
shown at the right, you form two triangles. Thus,
the sum of the measures of the interior angles
of a quadrilateral is 2 180°, or 360°.
In the figure at the right, find mE.
mEmFmGmH360°
mE 90° 50° 85°360°
mE 225°360°
mE 225° 225°360°
mE135°
Study this example.
Find the measure of each angle in the given figure.
x85°135°35°360°
x255°360°
x105°
z70°75°180°
z145°180°
z35°
y105°180°
y75°
yand x
are supplementary.
The sum of the measures
of the interior angles of a
quadrilateral is 360°.
The sum of the measures of the
interior angles of a triangle is 180°.
T
S U
R
P Q
55 ° 25 °
B
C
A D
F
H G
E
85 ° 50 °
90 °
?
K
M L
J
70 ° 85 °
35 °
135 °
z°
y° x°
2.2
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