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answers to unit 1 geometry basics homework 5 angle addition postulate

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Fichohidn

The measure of the angles are :

  • 25°
  • 129°
  • x = 107° ; y = z = 73°
  • 167°
  • 52°
  • Angle 1 = 109° ; Angle 2 = 71°

To find x :

A right angle = 90°

65 + x = 90

x = 90° - 65°

x = 25°

(2) :

Vertically opposite angles are equal :

Sum of angles at a point = 360°

[(51 × 2) + (2x)] = 360°

106° + 2x = 360°

2x = 360° - 102°

2x = 258°

x = 254° ÷ 2

x = 129°

(3.)

Verticaly opposite angles are equal :

107° = x°

y° = z°

(2y + (2 × 107)) = 360°

2y + 214° = 360°

2y = 360° - 214°

2y = 146°

y = 146° ÷ 2

y = 73°

y = z = 73°

4.)

Measure of supplementary angles = 180°

Let the measure of it's supplement = x

x + 13° = 180°

x = 180° - 13°

x = 167°

5.)

Complementary angles add up to 90°

Let the measure of it's complement = x

x + 38° = 90°

x = 90° - 38°

x = 52°

6.)

Sum of linear pair of angles = 180°

(5x + 9) + (3x + 11) = 180°

5x + 3x + 9 + 11 = 180

8x + 20 = 180

8x = 180 - 20

8x = 160

x = 160/8

x = 20°

Angle 1 = 5(20) + 9 = 109°

Angle 2 = 3(20) + 11 = 71°

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