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. the equation 52 + 90 + y = 180 demonstrates one way to solve for y, and y = 38. since x + y = 180

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In the right - angled triangle shown, the three interior angles are 52°, 90°, and \(y\). So, \(52 + 90+y=180\).

Step2: Solve for \(y\)

\[

$$\begin{align*} 52 + 90+y&=180\\ 142 + y&=180\\ y&=180 - 142\\ y&=38 \end{align*}$$

\]

Step3: Use linear - pair property

Since \(x\) and \(y\) form a linear pair (\(x + y=180\)), and \(y = 38\), then \(x=180 - y\).

Answer:

The equation \(52 + 90 + y = 180\) demonstrates one way to solve for \(y\), and \(y = 38^{\circ}\). Since \(x + y=180\), \(x = 142^{\circ}\). But among the given options, the correct one is: The equation \(52 + 90 + y = 180\) demonstrates one way to solve for \(y\), and \(y = 38^{\circ}\).