Question

Find the values of a and b. a The diagram is not drawn to scale. a = U b = U

Answer 1

Answer:

a = 36°

b = 144°

Step-by-step explanation:

Method 1

Number of sides = n = 10

Sum of interior angles = (n - 2) × 180°

                                     = (10 - 2) × 180°

                                     = 8 × 180°

                                     = 1440°

Interior angle = b = sum of interior angles ÷ number of sides

                          b = 1440 ÷ 10

                          b = 144°

              a + b = 180° (Sum of angles in the straight line)

         a + 144° = 180°

a + 144° - 144° = 180° - 144°

                    a = 36°

Method 2

Number of sides = 10

Exterior angle = a = 360° ÷ Number of sides

                           a = 360° ÷ 10

                           a = 36°

            a + b = 180° (Sum of angles in the straight line)

        36° + b = 180°

36° + b - 36° = 180° - 36°

                 b = 144°