Question

solve for x in the figure below.
(left triangle: right - angled, one angle 60°, side labeled x + 42)
solve for x in the figure below.
(right triangle: angle 130°, sides labeled 5x and 3x + 2)

Explanation:

Step1: Solve first triangle (right triangle)

In a right triangle, acute angles sum to $90^\circ$.
$x + 42 + 60 = 90$
Simplify: $x + 102 = 90$
$x = 90 - 102$
$x = -12$

Step2: Solve second triangle (sum to $180^\circ$)

Triangle interior angles sum to $180^\circ$.
$3x + 2x + 2 + 130 = 180$
Simplify: $5x + 132 = 180$
$5x = 180 - 132$
$5x = 48$
$x = \frac{48}{5} = 9.6$

Answer:

For the right triangle: $x = -12$
For the triangle with $130^\circ$ angle: $x = 9.6$ (or $\frac{48}{5}$)