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Angles

This text covers the fundamentals of angles, including their definitions, interior and exterior spaces, and the Angle Addition Postulate. It provides examples of how to identify angle components such as sides and vertices and classify angles by their measures (acute, right, obtuse, and straight). The text includes practical exercises for calculating unknown angle measures and understanding the concept of congruence and angle bisectors. Perfect for students looking to strengthen their geometry skills and comprehension of angles.

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Angles

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  1. Angles

  2. Angle An object that has two rays (called sides) with a common endpoint (called the vertex).

  3. A B C Example 1 Name each of the following: Sides:_____________________ Vertex:_________ Name:_____________________

  4. Interior of an Angle the space between the rays that create an angle.

  5. Exterior of an Angle the space that is outside of the rays

  6. R Q S P Example 2 How does the diagram in EXAMPLE 1 differ from the diagram in this example?

  7. R Q S P Example 3 A) Name a point in the interior of QPS in EXAMPLE 2. B) Name a point in the exterior of QPR in EXAMPLE 2.

  8. Adjacent To be next to. SHARING a side.

  9. Angle Addition Postulate The sum of two adjacent angles is equal to the largest angle.

  10. R Q S P If R is in the interior of QPS, then mQPR + mRPS = mQPS. ANGLE ADDITION POSTULATE: If mQPR + mRPS = mQPS, then R is in the interior of QPS.

  11. R Q S P If R is in the interior of QPS, then mQPR + mRPS = mQPS. ANGLE ADDITION POSTULATE: If mQPR + mRPS = mQPS, then R is in the interior of QPS.

  12. P R Q S Example 4 If mPQS = 77 and mPQR = 32, then find mRQS.

  13. A B O C Example 5 If mAOC = 70, mAOB =(x + 10), and mBOC =x, find: x = __________ mBOC = _______________ mAOB = _______________

  14. Acute Angle An angle measuring less than 90°

  15. Right Angle An angle whose measure is exactly 90°

  16. Obtuse Angle An angle measuring greater than 90° but less than 180°

  17. Straight Angle An angle measuring exactly 180°

  18. Y L 125 F 35 I T C NAME:_________ OR ______ MEASURE:________ CLASSIFICATION___________ NAME:_________ OR ______ MEASURE:________ CLASSIFICATION___________ R T X S N S NAME:_________ OR ______ MEASURE:________ CLASSIFICATION___________ NAME:_________ OR ______ MEASURE:________ CLASSIFICATION___________ For each of the following angles A) Name it. B) Tell whether its measure is <90, >90, =90, or = 180. C) Classify it.

  19. Congruent to be the same shape and same size.

  20. Angle Bisector a line, ray, or segment that divides an angle into two congruent angles.

  21. W X Z Y Example 7 If XZ is an angle bisector of WXY, name the two congruent angles that it forms.

  22. E G I F H Example 8 FG bisects EFH. Find the value of x. m EFG = (5x – 10); m GFH = (3x + 25)

  23. E G I F H Example 9 FG bisects EFH. Find the value of x. m GFH = (3x + 20); m EFH = (4x + 80)

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