Question

find the measure of angle ecg.

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So, the angle opposite to \(23^{\circ}\) (angle \(BCA\)) is also \(23^{\circ}\).

Step2: Use the right - angle property

Since \(\angle ECG+\angle BCA = 90^{\circ}\) (because \(\angle ECG\) and \(\angle BCA\) are complementary angles as \(\angle ECF = 90^{\circ}\)). Let \(\angle ECG=x\). Then \(x + 23^{\circ}=90^{\circ}\).

Step3: Solve for \(x\)

Subtract \(23^{\circ}\) from both sides of the equation \(x+23^{\circ}=90^{\circ}\). So, \(x=90^{\circ}-23^{\circ}\).

Answer:

\(67^{\circ}\)