Question

find the measure of the missing angles.
answer attempt 2 out of 3
$d = square^{circ}$ $e = square^{circ}$ $f = square^{circ}$

Explanation:

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

Vertical angles are equal. The angle with measure \(29^{\circ}\) and angle \(e\) are vertical angles. So \(e = 29^{\circ}\)

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

Complementary angles sum to \(90^{\circ}\). The right - angle is \(90^{\circ}\), and one part is \(49^{\circ}\). So \(f=90^{\circ}- 49^{\circ}=41^{\circ}\)

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

The sum of angles around a point is \(360^{\circ}\). But we can also use the fact that \(d + 29^{\circ}+49^{\circ}+90^{\circ}=180^{\circ}\) (a straight - line angle is \(180^{\circ}\)).

$$d=180^{\circ}-(29^{\circ}+49^{\circ}+90^{\circ})=180^{\circ}-168^{\circ} = 110^{\circ}$$

Answer:

\(d = 110^{\circ}\), \(e = 29^{\circ}\), \(f = 41^{\circ}\)