Question

look at the diagram.
which equation can be used to solve for ( x )?
( 2(x + 6) = 90 )
( 8x = 90 )
( 3x + 6 = 90 )
( 2x + 6 = 90 )
solve for ( x ).
( x = )

Explanation:

Step1: Set up angle sum equation

The two angles $\angle DHE = (2x)^\circ$ and $\angle EHF = (x+6)^\circ$ add up to $90^\circ$ (since $DH$ is perpendicular to $CF$).
$$2x + (x + 6) = 90$$
Simplify the left side:
$$3x + 6 = 90$$

Step2: Isolate the term with $x$

Subtract 6 from both sides.
$$3x = 90 - 6$$
$$3x = 84$$

Step3: Solve for $x$

Divide both sides by 3.
$$x = \frac{84}{3}$$

Answer:

For the equation question:

$3x + 6 = 90$

For the value of $x$:

$x = 28$