Let's analyze and solve the questions from the image you uploaded.

Question 6:

The figure shows two parallel lines $l_1 \parallel l_2$, and we're asked to find the value of $x$. From the diagram:

• There is an angle of $37^\circ$ on one side.
• Another angle of $58^\circ$ on the opposite side of $x$.

Since $l_1 \parallel l_2$, we know that alternate interior angles and corresponding angles are equal. Using the linear pair property:

$x = 180^\circ - (37^\circ + 58^\circ) = 180^\circ - 95^\circ = 85^\circ$

Thus, the correct answer is (b) 85°.

Question 7:

If a wheel has six spokes equally spaced, the total degrees in a circle is $360^\circ$. The angle between two adjacent spokes is:

$\frac{360^\circ}{6} = 60^\circ$

Thus, the correct answer is (c) 60°.

Question 8:

This question asks which statements are true based on the given figure with angles $a$, $b$, $c$, $d$, and $e$.

• Statement (i) $a + b = d + c$: This is true because vertically opposite angles are equal.
• Statement (ii) $a + c + e = 180^\circ$: This is true because the sum of the angles on a straight line is 180°.
• Statement (iii) $b + f = c + e$: This is also true because they represent alternate interior angles.

Thus, all statements are correct, and the answer is (d) (ii) and (iii) both.

Question 9:

The angle which is two times its complement is $x$. Let the complement of $x$ be $90^\circ - x$. According to the problem, $x = 2(90^\circ - x)$.

Solving this equation: $x = 180^\circ - 2x$ $3x = 180^\circ$ $x = 60^\circ$

Thus, the correct answer is (a) 60°.

Question 10:

The angle which is two times its supplement is $x$. Let the supplement of $x$ be $180^\circ - x$. According to the problem, $x = 2(180^\circ - x)$.

Solving this equation: $x = 360^\circ - 2x$ $3x = 360^\circ$ $x = 120^\circ$

Thus, the correct answer is (d) 120°.

Do you need more details on any of these explanations? Here are 5 related questions to further explore:

1. What are the properties of parallel lines and angles formed by transversals?
2. How do you derive the sum of angles in a straight line and around a point?
3. How do complementary and supplementary angles differ in terms of equations?
4. What is the geometric significance of spokes in a wheel being equally spaced?
5. How do vertical and alternate angles relate in geometry?

Tip: For solving problems involving angles and parallel lines, always look for corresponding, alternate interior, and vertically opposite angles to simplify the calculations.