Question

1. if ( mangle6 = 163^{circ} ), complete the table with the value of the missing angles.

Explanation:

Step1: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary angles.
\(m\angle1 + m\angle2=180^{\circ}\)
\(m\angle2 = 180^{\circ}-m\angle1\)
\(m\angle2=180 - 163=17^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle3\) and \(\angle6\) are vertical angles.
Vertical angles are equal.
\(m\angle3=m\angle6 = 163^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle4\) and \(\angle3\) are supplementary angles.
\(m\angle4=180^{\circ}-m\angle3\)
\(m\angle4 = 180 - 163=17^{\circ}\)

Step4: Find \(m\angle5\)

\(\angle5\) and \(\angle6\) are supplementary angles.
\(m\angle5=180^{\circ}-m\angle6\)
\(m\angle5 = 180 - 163=17^{\circ}\)

Step5: Find \(m\angle7\)

\(\angle7\) and \(\angle6\) are supplementary angles.
\(m\angle7=180^{\circ}-m\angle6\)
\(m\angle7 = 180 - 163=17^{\circ}\)

Step6: Find \(m\angle8\)

\(\angle8\) and \(\angle3\) are vertical angles.
Vertical angles are equal.
\(m\angle8=m\angle3 = 163^{\circ}\)

Answer:

a. \(m\angle1 = 163^{\circ}\)
b. \(m\angle2 = 17^{\circ}\)
c. \(m\angle3 = 163^{\circ}\)
d. \(m\angle4 = 17^{\circ}\)
e. \(m\angle5 = 17^{\circ}\)
f. \(m\angle7 = 17^{\circ}\)
g. \(m\angle8 = 163^{\circ}\)