Question

find all missing angles.
m<1= degrees
m<2= degrees
m<3= degrees
m<4= degrees
m<5= degrees
m<6= degrees

Explanation:

Step1: Find \(m\angle1\)

Use the fact that a straight - line angle is \(180^{\circ}\). So, \(m\angle1 = 180^{\circ}-129^{\circ}-35^{\circ}=180^{\circ}-(129^{\circ} + 35^{\circ})=180^{\circ}-164^{\circ}=51^{\circ}\)

Step2: Find \(m\angle2\)

Use the triangle - angle sum property (\(180^{\circ}\) in a triangle). The sum of angles in the triangle with \(\angle1\) and \(\angle2\) is \(180^{\circ}\). So, \(m\angle2=180^{\circ}-51^{\circ}-95^{\circ}=34^{\circ}\)

Step3: Find \(m\angle3\)

Use the triangle - angle sum property. Let's assume the triangle with \(\angle3\). \(m\angle3 = 180^{\circ}-47^{\circ}-95^{\circ}=38^{\circ}\)

Step4: Find \(m\angle4\)

Use the triangle - angle sum property. In the right - angled triangle (assuming the small triangle with \(\angle4\) and \(\angle3\)), \(m\angle4=90^{\circ}-38^{\circ}=52^{\circ}\)

Step5: Find \(m\angle5\)

Use the straight - line angle property. \(m\angle5 = 180^{\circ}-47^{\circ}-95^{\circ}=38^{\circ}\)

Step6: Find \(m\angle6\)

First, find \(m\angle7\). Since \(m\angle7 = 180^{\circ}-121^{\circ}=59^{\circ}\). Then, using the triangle - angle sum property in the triangle with \(\angle5\) and \(\angle7\), \(m\angle6=180^{\circ}-38^{\circ}-59^{\circ}=83^{\circ}\)

Answer:

\(m\angle1 = 51\) degrees, \(m\angle2 = 34\) degrees, \(m\angle3 = 38\) degrees, \(m\angle4 = 52\) degrees, \(m\angle5 = 38\) degrees, \(m\angle6 = 83\) degrees