Question

find the value of x.
(there is a diagram with lines and angles: at point h, there are lines: vertical line eh (up) and gh (down), horizontal line cf (left and right, with a right angle at h between cf and gh/eh). angle between eh and hd is (7x)°, angle between hd and hc is (2x + 9)°. we need to find x.)
x = \boxed{}

Explanation:

Step1: Identify angle sum

The angles around point \( H \) on the left of \( EH \) and above \( CH \) should sum to \( 90^\circ \) (since \( CH \perp FH \) and \( EH \perp FH \), so \( \angle EHC = 90^\circ \)). Thus, \( 7x + (2x + 9) = 90 \).

Step2: Solve the equation

Combine like terms: \( 9x + 9 = 90 \).
Subtract 9: \( 9x = 81 \).
Divide by 9: \( x = 9 \).

Answer:

\( x = 9 \)