Question

find the value of x. (16x - 4)° (9x - 6)° 58°

Explanation:

Step1: Identify Vertical Angles

The angle \( (16x - 4)^\circ \) and the angle formed by \( 58^\circ \) and \( (9x - 6)^\circ \) are vertical angles (since they are opposite each other when two lines intersect). So, \( 16x - 4 = 58 + 9x - 6 \).

Step2: Simplify the Equation

Simplify the right - hand side: \( 58-6 = 52 \), so the equation becomes \( 16x - 4=9x + 52 \).

Step3: Solve for \( x \)

Subtract \( 9x \) from both sides: \( 16x-9x - 4=9x - 9x+ 52 \), which gives \( 7x - 4 = 52 \).
Add 4 to both sides: \( 7x-4 + 4=52 + 4 \), so \( 7x=56 \).
Divide both sides by 7: \( x=\frac{56}{7}=8 \).

Answer:

\( x = 8 \)