Answer:
Step-by-step explanation:
18). l║m and a transverse is intersecting these lines.
(11y - 32)° = (6x + 7)° [Vertical angles]
-6x + 11y = 39 -------(1)
(3x - 16)° + (6x + 7)°= 180° [Same side exterior angles]
9x - 9 = 180
9x = 189
x = 21
Now substitute the value of x in the equation (1)
-6(21) + 11y = 39
11y = 39 + 126
y = 15
19). l║m and a transversal is intersecting these lines.
(8x - 14)° + (5y + 16)° = 180° [Linear pair of angles]
8x + 5y = 178 --------(1)
(8x - 14)° = (5x + 34)° [Alternate exterior angles]
8x - 5x = 48
3x = 48
x = 16
From equation (1)
8(16) + 5y = 178
128 + 5y = 178
5y = 178 - 128
y = 10
20). From the figure attached,
m∠CAB = (5y - 23)°
Since sum of interior angles of a triangle is 180°
m∠CAB + m∠ACB + m∠ABC = 180°
(5y - 23)° + (2x + 13)° + (47)° = 180°
2x + 5y = 143 ------(1)
(5y - 23)° = 3x°
3x - 5y = -23 -----(2)
Equation (1) + Equation (2)
(2x + 5y) + (3x - 5y) = 143 - 23
5x = 120
x = 24
From equation (1)
2(24) + 5y = 143
48 + 5y = 143
5y = 95
y = 19
