Angle Relationships Pre-Algebra.

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Presentation transcript:

Angle Relationships Pre-Algebra

Types of Angles Acute Less than 90° Right Exactly 90° Obtuse Greater than 90° Straight Exactly 180° Reflex Greater than 180° Full Rotation Exactly 360°

Adjacent angles are “side by side” and share a common ray. 15º 45º

These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

Complementary Angles sum to 90° 50° 40°

Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent

Supplementary Angles sum to 180° 150° 30°

Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

Vertical Angles are opposite one another. Vertical angles are congruent. 100° 100°

Vertical Angles are opposite one another. Vertical angles are congruent. 80° 80°

Interior Angles of Polygons Triangle Quadrilateral (Square, Rectangle, Parallelogram, Trapezoid) The sum of the interior angles of any polygon can be found with the following formula using the number of sides. Sum of Interior angles= (N – 2) x 180 N is the number of sides.

Practice Time!

1) Find the missing angle. ?° 36°

1) Find the missing angle. ?° 36° 90 ° – 36 = 54°

2) Find the missing angle. ?° 64°

2) Find the missing angle. ?° 64° 90 ° – 64° = 26°

3) Solve for x. 2x° 3x°

3) Solve for x. 2x° 3x° 3x° + 2x° = 90° 5x = 90 x =18

4) Solve for x. x + 25 2x + 5

4) Solve for x. x + 25 2x + 5 (2x + 5) + (x + 25) = 90 3x + 30 = 90

5) Find the missing angle. 168° ?°

5) Find the missing angle. 168° ?° 180° – 168° = 12°

6) Find the missing angle. ?° 58°

6) Find the missing angle. ?° 58° 180° – 58° = 122°

7) Solve for x. 5x 4x

7) Solve for x. 5x 4x 4x + 5x = 180 9x = 180 x = 20

8) Solve for x. 3x + 20 2x + 10

8) Solve for x. 3x + 20 2x + 10 (2x + 10) + (3x + 20) = 180

11) Find the missing angles. 70 ° 70 ° b° Hint: The 3 angles in a triangle sum to 180°. d ° 65 °

11) Find the missing angles. 70 ° 70 ° 40° Hint: The 3 angles in a triangle sum to 180°. 75 ° 65 °

12) Find the missing angles. 45 ° 50 ° b° Hint: The 3 angles in a triangle sum to 180°. d ° 75 °

12) Find the missing angles. 45 ° 50 ° 85° Hint: The 3 angles in a triangle sum to 180°. 20° 75 °

The End