Question

solve for x.
5)
7)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. For the first triangle, we have the equation $30+(66 + x)+90=180$.

Step2: Simplify the left - hand side of the equation

First, add the known angles: $30 + 66+90+x=180$. So, $186 + x=180$. Then, subtract 186 from both sides: $x=180 - 186=- 6$.

For the second triangle, using the angle - sum property of a triangle, we have the equation $90 + 55+(x + 44)=180$.

Step3: Simplify the left - hand side of the second triangle's equation

Add the known angles: $90+55 + 44+x=180$. So, $189+x=180$.

Step4: Solve for x

Subtract 189 from both sides: $x=180 - 189=-9$.

We'll consider the first triangle's solution process more closely.
The correct application of the angle - sum property for the first triangle:
$30+(66 + x)+90 = 180$
$186+x=180$
$x=180 - 186=-6$

Answer:

$x=-6$