Question

Parallel lines relay race
does anyone know how to solve these?

Answer 1

1. The value of x is equal to 14°.

2. The value of x is equal to 9°.

3. The value of x is equal to 17°.

4. The value of x is equal to 5°.

In Mathematics and Geometry, the alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:

By applying the alternate interior angles theorem to parallel lines l and m cut through by a transversal, we can logically deduce the following pair of congruent angles;

(9x + 13)° = (12x - 29)°

9x - 12x = -29 - 13

-3x = -42

x = 14

Part 2.

By using x equals 14 from above, we have;

(13x + 5)° + (8x - 14)° = 180° ⇒ (Consecutive interior angles theorem)

21x - 9 = 180

21x = 189°

x = 189/21

x = 9°

Part 3.

By using x equals 9 from above, we have;

(5x + 52)° = (9x - 16)° ⇒ (Corresponding angles theorem)

9x - 5x = 52 - 16

4x = 68°

x = 68/4

x = 17°

Part 4.

By using x equals 17 from above, we have;

(10x + 17)° = (12x + 7)° ⇒ (Alternate exterior angles theorem)

12x - 10x = 17 - 7

2x = 10°

x = 10/2

x = 5°

Answer 2

Explanation:

a). Lines 'l' and 'm' are the parallel lines and a transversal line is intersecting these lines.

(9x + 13)° = (12x - 29)° [Alternate interior angles]

9x - 12x = -29 - 13

-3x = -42

x = 14

2). By substituting x = 14 in the box.

(13x + 5)° + (8x - 14)° = 180° [Consecutive interior angles]

21x - 9 = 180

21x = 189

x = 9

3). By placing x = 9 in the box,

(5x + 52)° = (9x - 16)° [Corresponding angles]

5x - 9x = -52 - 16

-4x = -68

x = 17

4). By placing x = 17 in the box,

(10x + 17)° = (12x + 7)° [Alternate exterior angles]

10x - 12x = -17 + 7

-2x = -10

x = 5