Question

ex 1
find the value of x.
$(12x + 3)^{circ}$
$(13x + 2)^{circ}$

Explanation:

Step1: Identify polygon type, sum angles

The figure is a trapezoid (4-sided polygon). The sum of interior angles of an n-sided polygon is $(n-2)\times180^\circ$. For $n=4$:
$$(4-2)\times180^\circ = 360^\circ$$
Also, the two top angles are right angles ($90^\circ$ each) as indicated by the right-angle arrows.

Step2: Set up angle sum equation

Sum all interior angles equal to $360^\circ$:
$$90^\circ + 90^\circ + (12x+3)^\circ + (13x+2)^\circ = 360^\circ$$

Step3: Simplify and solve for x

Combine like terms:
$$180 + 12x + 3 + 13x + 2 = 360$$
$$25x + 185 = 360$$
Subtract 185 from both sides:
$$25x = 360 - 185$$
$$25x = 175$$
Divide by 25:
$$x = \frac{175}{25}$$

Answer:

$x=7$