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 = ° Vertically opposite angles are equal
Now, consider a║b and 'c' be a transversal then,
Statements Reasons
1. ∠XYZ = ∠QZU = ° Corresponding angles are equal
∴ m∠1 = °
2.∠PZA + ∠PZQ + ∠QZU = 180° Sum of angles on a straight line is 180°.
3. Substitution property
4. Combining like terms
5. Subtraction property of equality
∴
6. Division property of equality
Plug in , we get
= 56°
= 66°
So,
Hence, options (1), (2) , (7) and (8) are correct.
36 cm²s⁻¹ is the rate at which the area of the square is increasing.
Given each side of the square is increasing at a rate of 6cm/s
Area, A = s², s is the side length
=> {chain rule of differentiation}
= 6 cm/s
When A = 9 cm² => 9 = s²
=> s = √(9) => s = 3 cm
Hence, = 2 × 3 × 6 = 36 cm²s⁻¹
Hence, 36 cm²s⁻¹ is the rate at which the area of the square increases
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