Question

Help me with my geometry please

Answer 1

Answer:

see explanation

Step-by-step explanation:

the exterior angle = 180° - interior angle

(17)

exterior angle = 180° - 144° = 36°

The sum of the exterior angles of a polygon = 360°

Hence the number of sides n is

n = $\frac{360}{36}$ = 10

(18)

exterior angle = 180° - 156° = 24°

n = $\frac{360}{24}$ = 15

(19)

exterior angle = 180° - 160° = 20°

n = $\frac{360}{20}$ = 18

In the following 2 questions we are using that the sum of the interior angles of a quadrilateral is 360°

(20)

summing the angles and equating to 360

2x + 15 + 3x - 20 + x + x + 15 = 360

7x + 10 = 360 ( subtract 10 from both sides )

7x = 350 ( divide both sides by 7 )

x = 50

∠J = 2x + 15 = 100 + 15 = 115°

∠K = 3x - 20 = 150 - 20 = 130°

∠M = x = 50°

∠N = x + 15 = 50 + 15 = 65°

(21)

6x - 4 + 2x + 8 + 6x - 4 + 2x + 8 = 360

16x + 8 = 360 ( subtract 8 from both sides )

16x = 352 ( divide both sides by 16 )

x = 22

∠R = ∠T = 6x - 4 = 132 - 4 = 128°

∠S = ∠U = 2x + 8 = 44 + 8 = 52°