Angle 8 is 110° and lines P and Q are parallel. Find the measure of angle 2. Show your work how would you write this if the answer was 70 degrees

Answer 1

Given that angle 8 is \(110^\circ\) and lines P and Q are parallel, we need to find the measure of angle 2.

Assuming that angle 8 and angle 2 are on the same transversal line intersecting lines P and Q, we can use the properties of corresponding angles, alternate interior angles, or same-side interior angles to find angle 2.

Step-by-Step Solution:

1. Identify Relationship: Since lines P and Q are parallel, and we have angle 8 = \(110^\circ\), we need to identify how angle 2 is positioned relative to angle 8.

2. Determine the Type of Angle: If angle 2 is an interior angle on the same side of the transversal as angle 8 (same-side interior angles), then: \[ \text{same-side interior angles add up to } 180^\circ. \] Therefore, we can set up the equation: \[ \angle 2 + \angle 8 = 180^\circ. \] Substituting \( \angle 8 \): \[ \angle 2 + 110^\circ = 180^\circ. \]

3. Solve for Angle 2: \[ \angle 2 = 180^\circ - 110^\circ = 70^\circ. \]

Conclusion:

Thus, the measure of angle 2 is \(70^\circ\).

Final Answer:

\[ \angle 2 = 70^\circ. \]