The question is missing figure and the options. So, the figure is attached alongwith the options
Answer:
Correct options: (1), (2) , (7) and (8)
Step-by-step explanation:
Given:
Lines a and b are parallel.
Consider a║b and 'd' be a transversal then,
Statements Reasons
1. ∠BXZ = ∠AZP = 58° Corresponding angles are equal
∴ m∠2 = 58°
2. ∠BYC = ∠XYZ = [tex](4x-10)[/tex]° Vertically opposite angles are equal
Now, consider a║b and 'c' be a transversal then,
Statements Reasons
1. ∠XYZ = ∠QZU = [tex](4x-10)[/tex]° Corresponding angles are equal
∴ m∠1 = [tex](4x-10)[/tex]°
2.∠PZA + ∠PZQ + ∠QZU = 180° Sum of angles on a straight line is 180°.
3. [tex]58\° +(3x-1)\°+(4x-10)\° = 180\°[/tex] Substitution property
4. [tex]47\° + 7x= 180\°[/tex] Combining like terms
5. [tex]7x=180\°-47\°[/tex] Subtraction property of equality
∴ [tex]7x = 133\°[/tex]
6. [tex]x = 19\°[/tex] Division property of equality
Plug in [tex]x = 19\ in\ (3x-1)\°\ and\ (4x-10)\°[/tex], we get
[tex](3x-1)\° = (3(19)-1)\°[/tex] = 56°
[tex](4x-10)\° = (4(19)-10)\°[/tex] = 66°
So, [tex](3x-1)\° \ne (4x-10)\°[/tex]
Hence, options (1), (2) , (7) and (8) are correct.
