Question

angle relationships
boom cards
m∠lha = (27 + 2x)°
m∠bhq = 23 °
find x.
diagram of intersecting lines with a right angle at h between some lines

Explanation:

Step1: Identify angle sum relationship

$\angle BHQ + \angle LHA + 90^\circ = 180^\circ$

Step2: Substitute given angle values

$23^\circ + (27 + 2x)^\circ + 90^\circ = 180^\circ$

Step3: Simplify the left-hand side

$23 + 27 + 2x + 90 = 180$
$140 + 2x = 180$

Step4: Solve for $x$

$2x = 180 - 140$
$2x = 40$
$x = \frac{40}{2}$

Answer:

$20$