Question

find the value of each indicated angle.
1)
2)
3)
4)
5)
6)
8)

Explanation:

Step1: Use vertical - angle and supplementary - angle relationships

For problem 1:
The \(91^{\circ}\) angle and \(x\) are supplementary (they form a linear pair). So \(x = 180^{\circ}-91^{\circ}\).
\(x = 89^{\circ}\)

For problem 2:
The \(98^{\circ}\) angle and \(x\) are supplementary (they form a linear pair). So \(x=180^{\circ} - 98^{\circ}\).
\(x = 82^{\circ}\)

For problem 3:
The \(118^{\circ}\) angle and its adjacent angle (let's call it \(y\)) are supplementary. \(y = 180^{\circ}-118^{\circ}=62^{\circ}\). Then, since the two lines are parallel and we use the corresponding - angle relationship, \(x = y\). So \(x = 62^{\circ}\)

For problem 4:
Using the corresponding - angle relationship (since the two lines are parallel), \(x = 53^{\circ}\)

For problem 5:
The \(122^{\circ}\) angle and its adjacent angle (let's call it \(z\)) are supplementary. \(z = 180^{\circ}-122^{\circ}=58^{\circ}\). Then, since the two lines are parallel and we use the corresponding - angle relationship, \(x = z\). So \(x = 58^{\circ}\)

For problem 6:
The \(88^{\circ}\) angle and \(x\) are supplementary (they form a linear pair). So \(x = 180^{\circ}-88^{\circ}\).
\(x = 92^{\circ}\)

For problem 7:
The \(62^{\circ}\) angle and \(x\) are supplementary (they form a linear pair). So \(x = 180^{\circ}-62^{\circ}\).
\(x = 118^{\circ}\)

For problem 8:
The \(73^{\circ}\) angle and \(x\) are supplementary (they form a linear pair). So \(x = 180^{\circ}-73^{\circ}\).
\(x = 107^{\circ}\)

Answer:

1. \(89^{\circ}\)
2. \(82^{\circ}\)
3. \(62^{\circ}\)
4. \(53^{\circ}\)
5. \(58^{\circ}\)
6. \(92^{\circ}\)
7. \(118^{\circ}\)
8. \(107^{\circ}\)