Question

1 - 99 calculate all the missing angles in the diagram below
a.
b.
c. a and e are corresponding angles
d. c and d are a linear pair

Explanation:

Step1: Identify angle - pair relationships

Use properties of parallel lines and transversals (corresponding, alternate - interior, vertical, and supplementary angles).

Step2: Solve for angles in the first diagram

Let's assume the parallel lines and transversals in the first diagram.
For the \(85^{\circ}\) angle:

• Its vertical angle is also \(85^{\circ}\).
• The angle adjacent to the \(85^{\circ}\) angle on the same side of the transversal is \(180 - 85=95^{\circ}\) (supplementary angles).
• For the \(75^{\circ}\) angle, its vertical angle is \(75^{\circ}\), and the angle adjacent to it on the same side of the transversal is \(180 - 75 = 105^{\circ}\).

Step3: Solve for angles in the second diagram

In the second diagram with a \(30^{\circ}\) angle:

• Its vertical angle is \(30^{\circ}\).
• The angle adjacent to the \(30^{\circ}\) angle on the same side of the transversal is \(180 - 30=150^{\circ}\).
• For the \(110^{\circ}\) angle, its vertical angle is \(110^{\circ}\), and the angle adjacent to it on the same side of the transversal is \(180 - 110 = 70^{\circ}\).

Since no specific angles are named in the question, we have found all related angles based on angle - pair relationships.

Answer:

In the first diagram, the angles related to \(85^{\circ}\) are \(85^{\circ}\) (vertical), \(95^{\circ}\) (supplementary), and for \(75^{\circ}\) are \(75^{\circ}\) (vertical), \(105^{\circ}\) (supplementary). In the second diagram, for \(30^{\circ}\) are \(30^{\circ}\) (vertical), \(150^{\circ}\) (supplementary) and for \(110^{\circ}\) are \(110^{\circ}\) (vertical), \(70^{\circ}\) (supplementary).