Question

in the diagram shown, ( mangle xwz = 90^circ ). what is ( x )?

Explanation:

Step1: Sum of angles in right angle

Since \( m\angle XWZ = 90^\circ \), the sum of \( (5x + 5)^\circ \) and \( (2x + 8)^\circ \) is \( 90^\circ \). So, \( (5x + 5)+(2x + 8)=90 \).

Step2: Combine like terms

Combine the \( x \)-terms and constant terms: \( 5x+2x + 5 + 8=90 \), which simplifies to \( 7x+13 = 90 \).

Step3: Solve for x

Subtract 13 from both sides: \( 7x=90 - 13=77 \). Then divide both sides by 7: \( x=\frac{77}{7}=11 \).

Answer:

\( x = 11 \)