Question

find the measure of the missing angles.
answer attempt 1 out of 2
$x=\square{}^{circ}$ $y=\square{}^{circ}$

Explanation:

Step1: Find the value of \(x\)

Since \(x\) and \(40^{\circ}\) are complementary angles (they form a right - angle together), we use the formula \(x + 40^{\circ}=90^{\circ}\).
Subtracting \(40^{\circ}\) from both sides gives \(x=90^{\circ}-40^{\circ}\).

Step2: Find the value of \(y\)

We know that the sum of angles around a point is \(360^{\circ}\). Also, we have a right - angle (\(90^{\circ}\)) and the angle \(40^{\circ}\) and \(x = 50^{\circ}\).
Using the formula \(y+90^{\circ}+40^{\circ}+x = 180^{\circ}\) (since it's a linear pair of angles, sum is \(180^{\circ}\)). Substitute \(x = 50^{\circ}\) into the formula: \(y+90^{\circ}+40^{\circ}+50^{\circ}=180^{\circ}\), or \(y+180^{\circ}=180^{\circ}\) (another way: vertical angles and angle sum. Since \(x = 50^{\circ}\), and \(y\) and \(x + 40^{\circ}\) are supplementary. \(y+(x + 40^{\circ})=180^{\circ}\). Substitute \(x = 50^{\circ}\), we get \(y+90^{\circ}=180^{\circ}\))

Answer:

\(x = 50^{\circ}\), \(y = 130^{\circ}\)