Question

find all missing angles.
m<1= degrees
m<2= degrees
m<3= degrees
m<4= degrees

Explanation:

Step1: Find \(m\angle1\)

In a right - triangle, the sum of angles is \(180^{\circ}\). For the large right - triangle with one angle \(72^{\circ}\), \(m\angle1=180^{\circ}-90^{\circ}-72^{\circ}=18^{\circ}\)

Step2: Find \(m\angle4\)

For the large right - triangle, \(m\angle1 + 57^{\circ}+m\angle4=90^{\circ}\). Since \(m\angle1 = 18^{\circ}\), then \(m\angle4=90^{\circ}-(18^{\circ}+57^{\circ}) = 15^{\circ}\)

Step3: Find \(m\angle2\)

In the small right - triangle, \(m\angle2=90^{\circ}-72^{\circ}=18^{\circ}\)

Step4: Find \(m\angle3\)

Since \(m\angle3 + 57^{\circ}=90^{\circ}\), then \(m\angle3=90^{\circ}-57^{\circ}=33^{\circ}\)

Answer:

\(m\angle1 = 18\) degrees, \(m\angle2=18\) degrees, \(m\angle3 = 33\) degrees, \(m\angle4=15\) degrees