Question

find the measure of the missing angles.
answer attempt 1 out of 3
$d=square^{circ}$ $e=square^{circ}$ $f=square^{circ}$

Explanation:

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

Since \(d\) is a right angle (marked with the small square), by the definition of a right - angle, \(d = 90^{\circ}\).

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

Angles \(e\) and \(134^{\circ}\) are supplementary (they form a linear pair). Using the formula for supplementary angles \(e+134^{\circ}=180^{\circ}\). Solving for \(e\), we get \(e = 180^{\circ}-134^{\circ}=46^{\circ}\).

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

Angles \(e\) and \(f\) are supplementary (they form a linear pair). Using the formula for supplementary angles \(e + f=180^{\circ}\). Since \(e = 46^{\circ}\), then \(f=180^{\circ}-e\). Substituting \(e = 46^{\circ}\), we get \(f = 134^{\circ}\) (alternatively, \(f\) and \(134^{\circ}\) are vertical angles, and vertical angles are equal).

Answer:

\(d = 90^{\circ}\), \(e = 46^{\circ}\), \(f = 134^{\circ}\)