Question

1. find the value of x.

diagram: horizontal line, vertical line (right angle), angle (4x - 10)° between vertical and a ray, angle x° between that ray and horizontal. options: 55, 20, 70, 38

Explanation:

Step1: Identify angle sum

The right angle (90°), \((4x - 10)^\circ\), and \(x^\circ\) sum to 180° (straight line). So:
\(90 + (4x - 10) + x = 180\)

Step2: Simplify equation

Combine like terms:
\(90 - 10 + 4x + x = 180\)
\(80 + 5x = 180\)

Step3: Solve for x

Subtract 80:
\(5x = 180 - 80\)
\(5x = 100\)

Divide by 5:
\(x = \frac{100}{5} = 20\)

Answer:

20