6th Grade Math Textbook, Progress

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 mP
55° and mQ
25°, what is mR?

mPmQmR
180°

55°  25° mR
180°

80° mR
180°

80°80° mR
180°

mR
100°

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.

mEmFmGmH
360°

mE 90°  50°  85°
360°

mE 225°
360°

mE 225° 225°
360°

mE
135°

Study this example.

Find the measure of each angle in the given figure.

x85°135°35°
360°

x255°
360°

x
105°

z70°75°
180°

z145°
180°

z
35°

y105°
180°

y
75°

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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