3-3: The Angle Addition Postulate

Angle Addition Postulate◦ For any angle PQR, if A is in the interior of PQR,

then mPQA + mAQR = mPQR

◦ What does it mean?1) Two small angles that share a side can be

added together to find their combined, larger angle.

2) If you know the combined measure and one of the smaller angles, you can subtract to find the other small angle.

P

A

R

Q12

Angle Addition Postulate◦ For any angle PQR, if A is in the interior of PQR,

then mPQA + mAQR = mPQR

◦ What does it mean?1) Two small angles that share a side can be

added together to find their combined, larger angle.

2) If you know the combined measure and one of the smaller angles, you can subtract to find the other small angle.

P

A

R

Q12

Examples◦ If PQA = 35 and AQR = 40, find PQR

◦ PQR = PQA + AQR◦ PQR = 35 + 40 substitute◦ PQR = 75

◦ If PQR = 86 and AQR = 22, find PQA

◦ PQA =

P

A

R

Q12

64

This time, with some Algebra!◦ If ABD = 120, find ABC and CDB

◦ x = ◦ ABC = ◦ CDB =

183684

Just like every segment has a midpoint, every angle has a ray that bisects the angle. This ray is called the ANGLE BISECTOR.◦ If AT bisects CAN and

CAN = 130, find 1 & 2.

◦ Since AT bisects, 1 = 2◦ CAN = 1 + 2 Angle Addition Postulate◦ 130 = 1 + 1 Substitution◦ 130 = 2 1 Combine◦ 65 = 1 Divide both sides by 2◦ 1 and 2 both are 65˚

Assignment◦ Worksheet #3-3