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
