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Types of Angles and Their Properties

Explore different types of angles including complementary angles, supplementary angles, adjacent angles, straight angles, opposite rays, intersecting lines, and vertical angles. Understand their properties and relationships.

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Types of Angles and Their Properties

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  1. Angles that have a sum of 90° Angles that have a sum of 180° Angles that share a side. Two adjacent angles whose non-common sides form a line. Angles whose sides form two pairs of opposite rays.

  2. 52° 38° ∠ABD ∠BDC complementary 52° 128° ∠ABD ∠BDE supplementary ∠CDB ∠EDB adjacent

  3. 90° 57° 33° 90° m∠2 180° 41° 180° 41° 139°

  4. Complementary: ∠DEF & ∠B Supplementary: ∠FEG & ∠B Adjacent: ∠DEF & ∠FEG m∠1 + m∠2 = 90° m∠2 = 90° - m∠1 m∠2 = 90° - 73° m∠2 = 17° m∠3 + m∠4 = 180° m∠3 = 180° - m∠4 m∠3 = 180° - 37° m∠3 = 143°

  5. 180° 180° 3x + 8 4x - 3 180° 7x + 5 180° 7x 175° x 25 25 3x + 8 3(25) + 8 83° 4x - 3 4(25) - 3 97° 83° 97°

  6. m∠BCA + m∠DCA = 180° 5x + 1 + 6x + 3 = 180° 11x + 4 = 180° 11x = 176° x = 16 m∠DCA = 6x + 3 m∠BCA = 5x + 1 m∠DCA = 6(16) + 3 m∠BCA = 5(16) + 1 m∠DCA = 99° m∠BCA = 81°

  7. intersecting lines adjacent ∠1 ∠3 opposite rays ∠1 ∠2 ∠2 ∠3

  8. Linear Pairs: None Vertical Angles: ∠1 & ∠4, ∠2 & ∠5, ∠3 & ∠6

  9. 4x° 4x° supplementary x° 4x° 180° 5x° 180° x 36° 5 36° 4(36) 144°

  10. m∠1 = x° and m∠2 = 3x° m∠1 + m∠2 = 180° x + 3x = 180° 4x = 180° x = 45 m∠2 = 3x° m∠1 = x° m∠ = 45° m∠2 = 3(45) m∠2 = 135°

  11. coplanar collinear intersect adjacent straight angle interior

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