Question

question 3
what kind of angle is ∠acd?
image of angle diagram with points a, c, b on a horizontal line, e above c (right angle at c between a-c and c-e), and d as a point on a ray from c between c-e and c-b
options:
○ acute
○ supplementary
○ obtuse
○ complementary

Explanation:

1. First, identify the right angle at ∠ACE (since there's a right - angle symbol at C between AC and CE). A right angle is $90^{\circ}$.
2. The straight line AB means that ∠ACB is a straight angle, which is $180^{\circ}$.
3. ∠ACD is composed of the right angle ∠ACE and ∠ECD. Since ∠ACE is $90^{\circ}$ and ∠ECD is a positive angle, ∠ACD = ∠ACE+∠ECD> $90^{\circ}$. Also, ∠ACD < $180^{\circ}$ (because it is less than the straight angle ∠ACB).
4. An obtuse angle is defined as an angle whose measure is greater than $90^{\circ}$ and less than $180^{\circ}$. So, ∠ACD is an obtuse angle.

Answer:

Obtuse