What is the measure of angle 1?

Question

2 parallel lines are crossed by a transversal to form 8 angles. Clockwise from top left, the angles are blank, 92 degrees, blank, blank; blank, 2, 1, blank.
86°
88°
90°
92°

Answer 1

To find the measure of angle 1, we can use the properties of angles formed when a transversal crosses parallel lines.

1. The two parallel lines form alternate interior angles that are equal.
2. Corresponding angles are equal.
3. Consecutive interior angles are supplementary (they add up to 180°).

From the information given:

• We have angle 2 = 92° (the angle immediately clockwise from angle 1).

Since angle 1 and angle 2 are on the same side of the transversal and consecutive to each other, they are supplementary. Therefore, we can use the following equation:

Angle 1 + Angle 2 = 180°

Substituting the value of angle 2:

Angle 1 + 92° = 180°

Now, solving for angle 1:

Angle 1 = 180° - 92°
Angle 1 = 88°

So, the measure of angle 1 is 88°.