https://file.aiquickdraw.com/mathbot/file/1725936389950pe615r1l.jpg

Let's break down the problem:

We are given:
1. \( m\angle WXZ = (5x + 3)^\circ \)
2. \( m\angle ZXY = (8x - 4)^\circ \)
3. \( \angle WXY \) is a right angle, meaning \( m\angle WXY = 90^\circ \).

The diagram shows that:
- \( \angle WXY \) is the sum of \( \angle WXZ \) and \( \angle ZXY \), since they form a straight line at \( X \).

So, we can set up the equation:
\[
m\angle WXZ + m\angle ZXY = m\angle WXY
\]
Substitute the expressions:
\[
(5x + 3) + (8x - 4) = 90
\]
Now, let's solve for \( x \).

1. Combine like terms:
\[
5x + 8x + 3 - 4 = 90
\]
\[
13x - 1 = 90
\]

2. Add 1 to both sides:
\[
13x = 91
\]

3. Solve for \( x \):
\[
x = \frac{91}{13} = 7
\]

Now that we have \( x = 7 \), we can find the measures of \( \angle WXZ \) and \( \angle ZXY \).

- \( m\angle WXZ = 5x + 3 = 5(7) + 3 = 35 + 3 = 38^\circ \)
- \( m\angle ZXY = 8x - 4 = 8(7) - 4 = 56 - 4 = 52^\circ \)

Therefore:
- \( x = 7 \)
- \( m\angle WXZ = 38^\circ \)
- \( m\angle ZXY = 52^\circ \)

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How can you verify the solution using the sum of angles?
2. What happens if \( \angle WXY \) was not a right angle?
3. Can you find the value of \( x \) if \( \angle WXZ \) and \( \angle ZXY \) were given as actual measures?
4. What is the relationship between adjacent angles that form a straight line?
5. How would the problem change if a different expression for \( m\angle ZXY \) were given?

**Tip:** When dealing with angles in geometric figures, remember that angles on a straight line always add up to 180°, and angles in a triangle sum to 180°.

If m∠WXZ = (5x + 3)°, m∠ZXY = (8x - 4)°, and ∠WXY is a right angle, find each measure.

Solve the geometry problem where m∠WXZ = (5x + 3)°, m∠ZXY = (8x - 4)°, and ∠WXY is a right angle. Learn to calculate the value of x and the measures of each angle using algebraic and geometric principles. Suitable for 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