Question

question 4
what angle relationship do ∠acd and ∠dcb have?
image of angle diagram with points a, c, b on a straight line, c with a right angle to e, and a ray to d
options:

• congruent
• right angles
• linear pairs
• complementary

Explanation:

1. Recall the definition of a linear pair: Two adjacent angles that form a straight line (sum to \(180^\circ\)) are a linear pair.
2. In the diagram, \(\angle ACD\) and \(\angle DCB\) share a common side \(CD\), have a common vertex \(C\), and their non - common sides \(AC\) and \(CB\) form a straight line (since \(A - C - B\) is a straight line). So, they are adjacent and supplementary (sum to \(180^\circ\)), which fits the definition of a linear pair.
3. Congruent angles have equal measure, but there's no indication these angles are equal. Right angles are \(90^\circ\), and these angles sum to \(180^\circ\) (not necessarily each \(90^\circ\)). Complementary angles sum to \(90^\circ\), but these sum to \(180^\circ\), so they are not complementary.

Answer:

Linear Pairs