Question

1. find all missing angles. 11. m∠1=______ m∠2=____ m∠3=____ m∠4=____ m∠5=____ m∠6=____ m∠7=______

Explanation:

Step1: Find \(m\angle1\)

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

Step2: Find \(m\angle2\)

Use the angle - sum property of a triangle. Let the triangle with angles \(\angle1\), \(\angle2\) and the angle of \(95^{\circ}\) (the angle adjacent to \(\angle3\) which is vertical to the \(95^{\circ}\) - like angle). The sum of angles in a triangle is \(180^{\circ}\).
\(m\angle2=180^{\circ}-m\angle1 - 95^{\circ}\)
Substitute \(m\angle1 = 51^{\circ}\), then \(m\angle2=180^{\circ}-51^{\circ}-95^{\circ}=34^{\circ}\)

Step3: Find \(m\angle3\)

Use the vertical - angle theorem. Vertical angles are equal. So, \(m\angle3 = 180^{\circ}-95^{\circ}=85^{\circ}\)

Step4: Find \(m\angle4\)

Use the angle - sum property of a triangle. In the triangle with angles \(\angle3\), \(\angle4\) and \(47^{\circ}\)
\(m\angle4=180^{\circ}-m\angle3 - 47^{\circ}\)
Substitute \(m\angle3 = 85^{\circ}\), then \(m\angle4=180^{\circ}-85^{\circ}-47^{\circ}=48^{\circ}\)

Step5: Find \(m\angle7\)

Use the vertical - angle theorem. \(m\angle7=180^{\circ}-121^{\circ}=59^{\circ}\)

Step6: Find \(m\angle5\)

Use the vertical - angle theorem. \(m\angle5 = 47^{\circ}\) (vertical to the given \(47^{\circ}\) angle)

Step7: Find \(m\angle6\)

Use the angle - sum property of a triangle. In the triangle with angles \(\angle5\), \(\angle6\) and \(\angle7\)
\(m\angle6=180^{\circ}-m\angle5 - m\angle7\)
Substitute \(m\angle5 = 47^{\circ}\) and \(m\angle7 = 59^{\circ}\)
\(m\angle6=180^{\circ}-47^{\circ}-59^{\circ}=74^{\circ}\)

Answer:

\(m\angle1 = 51^{\circ}\)
\(m\angle2 = 34^{\circ}\)
\(m\angle3 = 85^{\circ}\)
\(m\angle4 = 48^{\circ}\)
\(m\angle5 = 47^{\circ}\)
\(m\angle6 = 74^{\circ}\)
\(m\angle7 = 59^{\circ}\)