Question

For questions 10 – 11, if l ||m, find the values of x and y

Answer 1

Answer:

10). x = 16

      y = 10

11). x = 24

    y = 19

Step-by-step explanation:

10). Since l ║ m and a line is transverse intersecting these parallel lines at two distinct points.

Two angles having measures (8x - 14)° and (5x + 34)°are the alternate exterior angles.

Since alternate interior angles are equal in measures.

Therefore, (8x - 14) = (5x + 34)

8x - 5x = 34 + 14

3x = 48

x = 16

Measure of angle (8x - 14)° = 8×16 - 14

                                            = 128 - 14

                                            = 114°

Sum of supplementary angles = 180°

Therefore, (8x - 14)° + (5y + 16) = 180°

                          114° + (5y + 16)°= 180°

                                              5y = 180 - 130

                                                y = 10

Therefore, x = 16 and y = 10

11). m∠BAC = (5y - 23)°

     m∠ACB = 47°

     m∠ABC = (2x + 13)°

Since these angles are the angles of a triangle,

(5y - 23)° + 47° + (2x + 13)° = 180°

5y + 2x = 180 - 37

2x + 5y = 143 ------(1)

Lines l ║ m and AC is a transverse,

3x = 5y - 23  [Exterior corresponding angles]

3x - 5y = -23 -----(2)

By adding equation (1) and (2)

(2x + 5y) + (3x - 5y) = 143 - 23

5x = 120

x = 24

From equation (1),

2(24) + 5y = 143

5y = 143 - 48

5y = 95

y = 19

Therefore, x = 24 and y = 19