https://file.aiquickdraw.com/mathbot/file/1726856396693yaecr74r.jpg

In this diagram, we are tasked with finding the value of \( w \), and we can see three angles: \( (5w + 5)^\circ \), \( (2w + 8)^\circ \), and the right angle (\( 90^\circ \)).

Since these three angles form a triangle, we can use the fact that the sum of the angles in any triangle is \( 180^\circ \).

So, we can set up the following equation:

\[
(5w + 5) + (2w + 8) + 90 = 180
\]

Now, let's solve this equation step-by-step.

### Step 1: Simplify the equation
Combine like terms:

\[
7w + 5 + 8 + 90 = 180
\]

\[
7w + 103 = 180
\]

### Step 2: Isolate \( w \)
Subtract 103 from both sides:

\[
7w = 180 - 103
\]

\[
7w = 77
\]

### Step 3: Solve for \( w \)
Now divide by 7:

\[
w = \frac{77}{7} = 11
\]

So, the value of \( w \) is \( 11 \).

Would you like a more detailed explanation or any further clarification?

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Here are 5 related questions:
1. How can we confirm that our solution for \( w \) is correct?
2. What happens if we substitute the value of \( w \) back into the expressions for the angles?
3. Can you solve similar problems involving exterior angles?
4. How would you solve a problem where the sum of the angles was not given as \( 180^\circ \)?
5. What other types of triangles can you solve if given expressions for the angles?

**Tip:** Always check your final solution by plugging the value back into the original expressions to confirm the angles sum to \( 180^\circ \).

Solve for the value of w in the diagram where the angles are given as (5w + 5)° and (2w + 8)°, with a right angle of 90°.

Learn how to solve for w in a triangle where the angles are given by expressions (5w + 5)° and (2w + 8)°, with one angle being 90°. This problem covers algebraic manipulation and the sum of angles in a triangle. Suitable for students in Grades 8-10.

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