Question

find the measure of the missing angles.
answer attempt 1 out of 2
$d=square ^{circ }$ $e=square ^{circ }$ $f=square ^{circ }$

Explanation:

Step1: Find the measure of angle \(d\)

From the figure, \(d\) is a right - angle. By the definition of a right - angle, \(d = 90^{\circ}\).

Step2: Find the measure of angle \(e\)

Angles \(e\) and \(151^{\circ}\) are supplementary (they form a linear pair). Using the formula for supplementary angles \(e+151^{\circ}=180^{\circ}\), we get \(e = 180^{\circ}-151^{\circ}=29^{\circ}\).

Step3: Find the measure of angle \(f\)

Angles \(e\) and \(f\) are vertical angles. By the vertical - angles theorem (vertical angles are congruent), \(f = e\). Since \(e = 29^{\circ}\), then \(f = 29^{\circ}\).

Answer:

\(d = 90^{\circ}\), \(e = 29^{\circ}\), \(f = 29^{\circ}\)