Question

if ( x = 34^{circ} ), find the measure of the angle in which ( ?^{circ} ) appears.

Explanation:

Step1: Recognize the right - angle relationship

In the given figure, the sum of the two angles \(x\) and \(?\) is \(90^{\circ}\) (since they form a right - angle).

Step2: Set up the equation

Let the unknown angle be \(y\). We know that \(x + y=90^{\circ}\). Given \(x = 34^{\circ}\), then \(y=90^{\circ}-x\).

Step3: Substitute the value of \(x\)

Substitute \(x = 34^{\circ}\) into the equation \(y = 90^{\circ}-x\). So \(y=90^{\circ}-34^{\circ}\).

Step4: Calculate the value of \(y\)

\(y = 56^{\circ}\)

Answer:

\(56^{\circ}\)