Question

1. solve for the value of x in the diagram below. enter each line of work as an equation.

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of the interior angles of a quadrilateral is $(4 - 2)\times180^{\circ}=360^{\circ}$.

Step2: Set up the equation

We have the angles $30^{\circ}$, $155^{\circ}$, $80^{\circ}$ and $x^{\circ}$. So the equation is $30 + 155+80 + x=360$.

Step3: Simplify the left - hand side

$30+155 + 80=265$, so the equation becomes $265+x = 360$.

Step4: Solve for x

Subtract 265 from both sides: $x=360 - 265$.
$x = 95$.

Answer:

$x = 95$