Special pairs of angles

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Presentation transcript:

Special pairs of angles

Adjacent Angles • Have a common vertex and a common side.

•. Complementary angles. •. Add up to 90o. •. 34o and 56o are • Complementary angles • Add up to 90o • 34o and 56o are complementary. • The complement of 70o is 20o.

Angles that are both complementary and adjacent together form a right angle.

•. Supplementary angles. •. Add up to 180o. •. 115o and 65o are • Supplementary angles • Add up to 180o • 115o and 65o are supplementary. • The supplement of 40o is 140o.

•. Linear Pair. •. Two adjacent. angles. that together. form a line. • • Linear Pair • Two adjacent angles that together form a line • The angles in a linear pair are always supplementary.

Solve for x, and find the size of the angles.

4x + 20 + x – 10 = 180 5x + 10 = 180 5x = 170  x = 34

Since x = 34 … 4x + 20 = 156 x – 10 = 24

•. Vertical angles. •. When lines cross, the. angles that are across • Vertical angles • When lines cross, the angles that are across from each other are vertical angles.

• The name comes from the fact that they only touch at the vertex.

• Vertical angles always are congruent.

Solve for x.

Solve for x. x = 45

Angle Bisector  A ray that divides an angle into two congruent angles

REMEMBER … adjacent complementary supplementary linear pair vertical angles angle bisector