What is the sum of the measures of the angles in a quadrilateral and in a decagon? step by step plz.

1800°

Step-by-step explanation:

The sum of angle in any n sided plane figure is given by the formula

(n - 2)180

where n is the number of side

Therefore, for a quadrilateral which has 4 sides,

n = 4

sum of angles in a quadrilateral = (4 - 2)180°

                                                     = 2 × 180

                                                     = 360°

for a decagon which has 10 sides

n = 10

sum of angles in a decagon = (10 - 2)180°

                                                     = 8 × 180

                                                     = 1440°

The sum of the measures of the angles in a quadrilateral and in a decagon

= 360° + 1440°

= 1800°