1. In the figure below, Line ET intersects with Line MN at B. The measure of Angle
KBM is 30 degrees. Angle EBM and Angle NBT are vertical angles. What is the
value of Angle NBE?

<NBE = 120°

Step-by-step explanation:

From the above attachment,

<KMB = 30°

<KBT = 90° (perpendicular angles are equal to 90°)

<MBE = x

<KMB + <KBT + <MBE = 180° (angles on a straight line are equal to 180°)

30° + 90° + <MBE = 180°

120° + <MBE = 180°

Solve for <MBE

<MBE = 180° - 120°

<MBE = 60°

<MBE = <TBN (vertical angles are congruent, making them equal to each other).

<TBN = 60°

<TBN + <NBE = 180° (angles on a straight line are equal to 180°)

60° + <NBE = 180°

<NBE = 180° - 60°

<NBE = 120°

Angle <NBE is equal to 120°

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction