https://file.aiquickdraw.com/mathbot/file/1727113161355ma8mws4x.jpg

Let's solve each question step by step.

### Question 3:
We have two angles inside a circle: \(2x\) and \(3x\), which are adjacent and sum to 90° as they form a right angle at the point where they meet the straight line.

Since the sum of these angles must equal 90° (a right angle):

\[
2x + 3x = 90^\circ
\]

Simplify the equation:

\[
5x = 90^\circ
\]

Solving for \(x\):

\[
x = \frac{90^\circ}{5} = 18^\circ
\]

So, the value of \(x\) is **18 degrees**.

### Question 4:
The diagram shows a right-angled triangle with sides labeled as \(3x\), \(4x\), and the area of the triangle given as 294 cm².

The formula for the area of a triangle is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Here, the base is \(4x\) and the height is \(3x\), so we can set up the equation:

\[
\frac{1}{2} \times 4x \times 3x = 294
\]

Simplifying:

\[
2 \times 12x^2 = 294
\]

\[
12x^2 = 294
\]

Now solve for \(x^2\):

\[
x^2 = \frac{294}{12} = 24.5
\]

Taking the square root of both sides:

\[
x = \sqrt{24.5} \approx 4.95
\]

So, the value of \(x\) is approximately **4.95**.

---

Do you have any questions or would you like further details on these solutions?

Here are five related questions:
1. How can we check that the sum of the angles in a triangle is always 180°?
2. What would change if the angle in Question 3 were not a right angle?
3. Can you derive the formula for the area of a right-angled triangle?
4. What is the geometric significance of the angles in a circle as seen in Question 3?
5. How does the Pythagorean theorem apply to Question 4?

**Tip:** For right-angled triangles, always think about applying either the Pythagorean theorem or area formulas depending on the given information.

The image contains two questions. Question 3 involves angles inside a circle and adjacent angles summing up to 90°, and Question 4 involves a right-angled triangle where the area and sides are given in terms of 'x'. The task is to find the value of 'x'.

Solve two math problems involving angles in a circle summing to 90°, and a right-angled triangle with given area to find the value of 'x'. These problems cover key concepts in geometry and algebra, using formulas for the sum of angles and the area of triangles.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation