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Angles Relationships

Angles Relationships. Unit 7 Math 7. Angle Relationships – Warm UP. Find the measure of angle 1 if the measure of angle 4 = 135 o Angles 1 and 4 are _______________ angles. If they are supplementary angles, they must add up to _________degrees. Angle Relationships. Let’s Review…

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Angles Relationships

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  1. Angles Relationships Unit 7 Math 7

  2. Angle Relationships – Warm UP • Find the measure of angle 1 if the measure of angle 4 = 135o • Angles 1 and 4 are _______________ angles. • If they are supplementary angles, they must add up to _________degrees.

  3. Angle Relationships Let’s Review… • Adjacent Angles: • two angles that share a vertex and a side but no points in their interiors. • Vertical Angles: • angles formed by two intersecting lines, and are opposite each other. Vertical angles are congruent. • Congruent Angles: • angles that have the same measure

  4. Angle Relationships • Supplementary Angles: • two angles whose measures add to 180° • Complementary Angles: • two angles whose measures add to 90°

  5. Angle Relationships supplementary Example 2: • Find the measure of angles 2, 3, and 4 if 1 = 43o • Angles 1 and 2 are _______________ angles. • If they are supplementary angles, they must add up to 180 degrees. Angle 2 measures 137 degrees.

  6. Angle Relationships Example 3 – • Find the measure of each angle • Angle HPM – • 108 degrees • Angle JPI – • 38 degrees

  7. Angle Relationships Example 3 – • Find the measure of each angle • Angle IPH – • 34 degrees • Angle KPL – • 34 degrees

  8. Let’s Review Packet from Last week

  9. EQ: How can we find missing angles using rules of geometry?

  10. Find the complement of... 1) 20 70 2) 47 43 No complement 3) 100

  11. Find the supplement of the given angle. 1) 40 140 5) 89 91 2) 18 162 6) 23 157 3) 153 27 7) 131 49 4) 65 115 8) 118 62

  12. The easiest way to find the missing measure(s) of an angle is to set up an equation and solve. For example:

  13. - Angles whose sum is 90 . Complementary Angles b a x+ 40 = 90 - 40 -40 x 40 x = 50

  14. Supplementary Angles - Angles whose sum is 180oFind the value of x. x 30 x + 30 = 180 - 30 - 30 x = 150

  15. (Guided Practice) Write a variable equation and solve. Find an angle whose supplement is 30 less than twice the angle. x 2x - 30 x + (2x - 30) = 180 3x - 30 = 180 +30 +30 3x = 210 70 x = 70

  16. Write a variable equation and solve. Find an angle whose complement is 20 more than three times the angle. x + 3x + 20 = 90 x 4x + 20 = 90 3x + 20 - 20 -20 4x = 70 4 4 x = 17.5

  17. Vertical Angles Theorem - the opposite angles of intersecting lines must be equal.

  18. Vertical Angles Theorem - the opposite angles of intersecting lines must be equal. Find the missing angles a, b and c. What’s the relationship between angles a and b? 25 155 b c a 155 25

  19. Summary Name some ways in which we can find the missing measure of an angle?

  20. Independent Practice/HW

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