https://file.aiquickdraw.com/mathbot/file/1726792942533z9h05875.jpg

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.

What is the value of x when two parallel lines form angles of 37° and 58° in a diagram, and solve additional angle-related geometry problems?

Learn how to find the value of angles formed by parallel lines and calculate complementary and supplementary angles. This problem explores key geometry concepts, including the Linear Pair Theorem, Complementary Angles, and Supplementary Angles Theorem. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation