Question

angle relationships
boom cards
m∠lha = (27 + 2x)°
m∠bhq = 23 °
find x.
(there is a diagram with lines intersecting at point h, with a right angle symbol between lh and ha, and points l, s, a, c, b, q on the lines.)

Explanation:

Step1: Identify vertical angles

$\angle BHQ$ y $\angle AHS$ son ángulos opuestos por el vértice, así que $m\angle AHS = m\angle BHQ = 23^\circ$

Step2: Use right angle sum

$\angle LHA$ y $\angle AHS$ forman un ángulo recto ($90^\circ$), así que su suma es $90^\circ$:
$$(27 + 2x) + 23 = 90$$

Step3: Simplify the equation

Sumar los términos constantes:
$$2x + 50 = 90$$

Step4: Isolate the variable term

Restar 50 de ambos lados:
$$2x = 90 - 50 = 40$$

Step5: Solve for x

Dividir entre 2:
$$x = \frac{40}{2} = 20$$

Answer:

$x = 20$