i need help quick!! this is unit 1:geometry basics. homework 5: angle relationships if anyone know tell me

The answers of the geometry exercise are :

1.) x = 25° ;

2.) x = 129°

3.) x = 73° ; y = 107° ; z = 73°

4.) s = 167°

5.) s = 52°

6.) M1 = 109° ; M2 = 79°

7.) M2 = 84°

1.)

The angle is right angled, which means the angle equals 90°

Hence,

x° + 65° = 90°

x = 90° - 65°

x = 25°

2.)

Vertically opposite angles are the same ; and the sum of angles at a point is 360°

Hence,

(51° × 2) + (2x) = 360°

102° + 2x = 360°

2x = 360° - 102°

2x = 258°

x = 258° / 2

x = 129°

3.)

y = 107° (Vertically opposite angles)

z = x (vertically opposite angles)

z = 2x

2x + (2 × 107) = 360°

2x + 214 = 360

2x = 360 - 214

2x = 146

x = 146 / 2

x = 73°

x = z = 73°

4.)

Let second angle = s

(s + 13) = 180 (Supplementary angles sums up to 180°)

s = 180 - 13 = 167°

5.)

Let second angle = s

(s + 38) = 90 (Complementary angles sums up to 90°)

s = 90 - 38 = 52°

6.)

Sum of Linear pair of angles = 180°

Hence,

(5x + 9) + (3x + 11) = 180

5x + 9 + 3x + 11 = 180

8x + 20 = 180

8x = 180 - 20

8x = 160

x = 20°

M1 = (5(20) + 9) = 100 + 9 = 109°

M2 = (3(20) + 11) = 60 + 11 = 71°

7.)

M1 = M2 (vertical angles are equal)

(17x + 1) = (20x - 14)

17x - 20x = - 14 - 1

-3x = - 15

x = 5

M2 = (20(5) - 14) = 100 - 14 = 84°

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