Question

1. find all missing angles.

11.
m∠1=
m∠2=
m∠3=
m∠4=
m∠5=
m∠6=
m∠

Explanation:

Step1: Find \(m\angle1\)

Use the property that the sum of angles on a straight - line is \(180^{\circ}\).
\(m\angle1 + 129^{\circ}=180^{\circ}\)
\(m\angle1=180^{\circ}- 129^{\circ}=51^{\circ}\)

Step2: Find \(m\angle2\)

Use the angle - sum property of a triangle (\(180^{\circ}\)) for the left - hand triangle. Let the third angle of the left - hand triangle be \(x\), and \(x = 180^{\circ}-95^{\circ}=85^{\circ}\) (linear pair). Then \(m\angle1+m\angle2 + x=180^{\circ}\). Substitute \(m\angle1 = 51^{\circ}\) and \(x = 85^{\circ}\).
\(51^{\circ}+m\angle2+85^{\circ}=180^{\circ}\)
\(m\angle2=180^{\circ}-(51^{\circ}+85^{\circ})=44^{\circ}\)

Step3: Find \(m\angle3\)

Use the angle - sum property of a triangle (\(180^{\circ}\)) for the upper - middle triangle. Let the third angle of the upper - middle triangle be \(y\), and \(y = 180^{\circ}-95^{\circ}=85^{\circ}\) (linear pair). Then \(m\angle3 + 47^{\circ}+y = 180^{\circ}\). Substitute \(y = 85^{\circ}\)
\(m\angle3=180^{\circ}-(47^{\circ}+85^{\circ})=48^{\circ}\)

Step4: Find \(m\angle4\)

Use the angle - sum property of a triangle (\(180^{\circ}\)) for the upper - middle triangle. \(m\angle3 + 47^{\circ}+m\angle4=180^{\circ}\). Substitute \(m\angle3 = 48^{\circ}\)
\(48^{\circ}+47^{\circ}+m\angle4=180^{\circ}\)
\(m\angle4=180^{\circ}-(48^{\circ}+47^{\circ})=85^{\circ}\)

Step5: Find \(m\angle5\)

Use the property of vertical angles (vertical angles are equal). The angle adjacent to \(47^{\circ}\) in the upper - middle triangle and \(\angle5\) are vertical angles. First, find the angle adjacent to \(47^{\circ}\) in the upper - middle triangle: \(180^{\circ}-(48^{\circ}+85^{\circ}) = 47^{\circ}\) (angle - sum property). Then, since \(\angle5\) and the non - \(47^{\circ}\), non - \(m\angle3\), non - \(m\angle4\) angle of the upper - middle triangle are vertical angles, \(m\angle5 = 47^{\circ}\)

Step6: Find \(m\angle7\)

Use the property that the sum of angles on a straight - line is \(180^{\circ}\). \(m\angle7+121^{\circ}=180^{\circ}\)
\(m\angle7=180^{\circ}-121^{\circ}=59^{\circ}\)

Step7: Find \(m\angle6\)

Use the angle - sum property of a triangle (\(180^{\circ}\)) for the right - hand triangle. \(m\angle5+m\angle6+m\angle7=180^{\circ}\). Substitute \(m\angle5 = 47^{\circ}\) and \(m\angle7 = 59^{\circ}\)
\(47^{\circ}+m\angle6+59^{\circ}=180^{\circ}\)
\(m\angle6=180^{\circ}-(47^{\circ}+59^{\circ})=74^{\circ}\)

Answer:

\(m\angle1 = 51^{\circ}\), \(m\angle2 = 44^{\circ}\), \(m\angle3 = 48^{\circ}\), \(m\angle4 = 85^{\circ}\), \(m\angle5 = 47^{\circ}\), \(m\angle6 = 74^{\circ}\), \(m\angle7 = 59^{\circ}\)