Question

consider the image. which equation demonstrates how to solve for x, and what is the value of x? the equation 52 + 90 + x = 180 demonstrates one way to solve for x, and x = 38. the equation 52 + 90 + x = 90 demonstrates one way to solve for x, and x = 52. the equation 52 + 90 + y = 90 demonstrates one way to solve for y, and y = 52. since x + y = 180, x = 128. the equation 52 + 90 + y = 180 demonstrates one way to solve for y, and y = 38. since x + y = 180, x = 142

Explanation:

Step1: Find angle y

In a right - angled triangle, the sum of the interior angles is 180°. Given one angle is 90° and another is 52°. So, using the angle - sum property of a triangle ($52 + 90+y=180$). Solving for y:
$y=180-(52 + 90)=180 - 142=38^{\circ}$

Step2: Find angle x

Since x and y are supplementary (a straight - line angle is 180°), we have the equation $x + y=180$. Substituting y = 38° into the equation, we get $x=180 - y$. So $x = 180-38 = 142^{\circ}$

Answer:

The equation $52 + 90 + y=180$ demonstrates one way to solve for y, and $y = 38^{\circ}$. Since $x + y=180$, $x = 142^{\circ}$