ANGLES OF TRIANGLES

THM 4.1-ANGLE SUM THEOREMThe Sum of the measure of the interior Angles of a

Triangle is ALWAYS 180°

180A B C o

A

BC

THM 4.1-ANGLE SUM THEOREMExample Problem: Find x

(3x+5)°

x°55°

Step 1Use Angle Sum Theorem that interior angles of triangle ALWAYS sum to 180°

Step 2Write Equation55+3x+5+x=180

Step 3Use Algebra to Solve for x

60+4x=1804x=120x=30

Step 4Now that we know x=30° we can find the measure of all the interior angles.

(3x+5)°

x°55°

Step 5Solving for Shaded Angle with x=30°

(3(30)+5)=95°

Step 6We now know the values of all the angles

Check to make sure they sum 180°95+55+30= 180°

55° 30°

95°

THM 4.2-THIRD ANGLE THEOREMIf two angles of one triangle are congruent to two

angles of a second triangle, then the third angles of the triangles are congruent.

EXTERIOR ANGLES

•Exterior Angle: the angles formed by one side of a triangle and the extension of another side.

Exterior Angle

REMOTE INTERIOR ANGLES

•Remote InteriorAngles: the interior angles of the triangle NOT adjacent to a given exterior angle.

Remote Interior Angle

2

THM 4.3-EXTERIOR ANGLE THEOREM

• The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles.

2

3

3

1 2 3

1

EXAMPLE-EXTERIOR ANGLE THEOREM

• Find the measure of the exterior angle x

x

20°

80°

20 80x o o

100x o

Step 1Use Exterior Angle Theorem to write Equation.

Step 2Use Algebra to Solve Equation

The End

Homework

Worksheet Page 192: 1-5 ALLWorksheet Page 193: 1(a-d)