Question

the measures of the angles of a triangle are shown in the figure below. solve for $x$.
the triangle has angles: $41^\circ$, $(4x+14)^\circ$, $83^\circ$

Explanation:

Step1: Sum triangle angles to 180°

$41 + 83 + (4x + 14) = 180$

Step2: Simplify left side

$41+83+14+4x = 138 + 4x$
$138 + 4x = 180$

Step3: Isolate term with x

$4x = 180 - 138$
$4x = 42$

Step4: Solve for x

$x = \frac{42}{4}$
$x = 10.5$

Answer:

$10.5$