Question

1. which of the following are true statements? select two that apply. (lesson 4.1) (1 point)

a) \\( \angle 5 \\) and \\( \angle 1 \\) are complementary.
b) \\( \angle 5 \\) and \\( \angle 1 \\) are supplementary.
c) \\( \angle 3 \\) and \\( \angle 4 \\) form a linear pair.
d) \\( \angle 4 \\) and \\( \angle 1 \\) form a linear pair.

Explanation:

Step1: Recall definitions

• Complementary angles: Two angles whose sum is \(90^{\circ}\).
• Supplementary angles: Two angles whose sum is \(180^{\circ}\).
• Linear - pair: Two adjacent angles that form a straight line (sum is \(180^{\circ}\)).

Step2: Analyze Option A

• \(\angle5\) and \(\angle1\): The sum of \(\angle5\) and \(\angle1\) is \(90^{\circ}\) (from the right - angle in the figure). So, \(\angle5\) and \(\angle1\) are complementary.

Step3: Analyze Option B

• \(\angle3\) and \(\angle4\): \(\angle3\) and \(\angle4\) are adjacent and form a straight line. So, \(\angle3+\angle4 = 180^{\circ}\), and they form a linear pair.

Answer:

A. \(\angle5\) and \(\angle1\) are Complementary.
B. \(\angle3\) and \(\angle4\) form a Linear Pair.