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Brainstorm

Brainstorm. What are different ways we can find the missing angles of a triangle or intersecting lines?. Complementary angles = 90°. Supplementary angles = 180°. Vertical angles are equal to each other. Alternate interior and exterior angles of parallel lines are equal. Definition.

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Brainstorm

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  1. Brainstorm • What are different ways we can find the missing angles of a triangle or intersecting lines? Complementary angles = 90° Supplementary angles = 180° Vertical angles are equal to each other Alternate interior and exterior angles of parallel lines are equal

  2. Definition • Quadrilateral – a polygon with 4 angles and 4 straight sides. All the angles add together to equal 360º 90º 90º 90º 90º

  3. Finding the Fourth Angle of a Quadrilateral The sum of the interior angles of a quadrilateral are equal to 360°. To find the fourth angle of a quadrilateral when the other three angles are known, subtract the number of degrees in the other three angles from 360°. Example: How many degrees are in the fourth angle of a quadrilateral whose other three angles are 80° and 110° and 95°? Answer: 360° - 80° - 110° - 95° = 75°

  4. What is the missing angle? 90º 90º 90º 90º 90º + ? 90º ? 360º

  5. Finding Missing Angle Measures of Quadrilaterals

  6. Opposite angles of parallelograms are equal. If you divide a parallelogram into two triangles they are congruent, so their angles also have to be congruent. Remember parallel lines cut by a transversal? Brainstorm with the person next to you: What do you think I can prove if I divide this parallelogram in half from the 65° to the y?

  7. Finding Missing Angle Measures of Quadrilaterals • Two ways to solve: • Using rules about opposite angles of parallelograms. • Using algebra and rules about angle measures of quadrilaterals.

  8. There is also a theorem in geometry that tells us that in all quadrilaterals, the sum of the measures of the angles is 360o.  This can be used in many situations, including problems where you need to find the measures of angles. 1. Problem: Find the measure of angle x.

  9. Find the missing angle measures:Draw the figure first. 88° 79°

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