Question

find the measure of the missing angles. answer ( d=square^{circ} quad e=square^{circ} quad f=square^{circ} )

Explanation:

Step1: Find the measure of \(d\)

Since \(d\) is a right - angle (as indicated by the square symbol), by the definition of a right - angle, \(d = 90^{\circ}\).

Step2: Find the measure of \(f\)

\(f\) and \(119^{\circ}\) are supplementary angles (they form a linear pair). Using the formula for supplementary angles \(a + b=180^{\circ}\), where \(a = 119^{\circ}\) and \(b = f\). So \(f=180^{\circ}-119^{\circ}\).

$$f = 61^{\circ}$$

Step3: Find the measure of \(e\)

\(e\) and \(f\) are vertical angles. By the vertical - angles theorem (vertical angles are equal), since \(f = 61^{\circ}\), then \(e=f\).

$$e = 61^{\circ}$$

Answer:

\(d = 90^{\circ}\), \(e = 61^{\circ}\), \(f = 61^{\circ}\)