Question

angle acb and ∠acd are , so their measures have a sum of . the measure of ∠acb is . so, the sum of the measures of ∠acb, ∠cba and ∠bac is , and the sum of the interior angles of △abc is . options: 90°, congruent angles, vertical angles, 180°, a linear pair, 65°, 25°

Explanation:

Step1: Identify angle relationship

Angle \( \angle ACB \) and \( \angle ACD \) form a linear pair, so their sum is \( 180^\circ \). Given \( \angle ACD = 155^\circ \), we calculate \( \angle ACB \) as \( 180^\circ - 155^\circ = 25^\circ \).

Step2: Analyze triangle \( \triangle ABC \)

In \( \triangle ABC \), \( \angle ABC = 90^\circ \) (right angle), \( \angle BAC = 65^\circ \), and we found \( \angle ACB = 25^\circ \). The sum of interior angles of a triangle is \( 180^\circ \). Let's verify: \( 90^\circ + 65^\circ + 25^\circ = 180^\circ \), which holds.

Answer:

• Angle \( ACB \) and \( \angle ACD \) are a linear pair, so their measures have a sum of \( 180^\circ \). The measure of \( \angle ACB \) is \( 25^\circ \).
• The sum of \( \angle ACB \), \( \angle CBA \), and \( \angle BAC \) is \( 180^\circ \), and the sum of the interior angles of \( \triangle ABC \) is \( 180^\circ \).