Question

angle relationships
boom cards
m∠qhl = (2x + 1)°
m∠sha = 31°
find x.
diagram of intersecting lines with right angle symbol

Explanation:

Step1: Identify complementary angles

$\angle QHL + \angle QHS = 90^\circ$

Step2: Substitute vertical angle for $\angle QHS$

$\angle QHS = \angle SHA = 31^\circ$

Step3: Set up equation for $x$

$2x + 1 + 31 = 90$

Step4: Simplify and solve for $x$

$2x + 32 = 90 \implies 2x = 58 \implies x = \frac{58}{2}$

Answer:

$29$