Question

the figure we constructed yesterday (see image below) features several types of angles and angle pairs.
angle classification
angles can be classified according to their measures.

• acute angle - angle that measures more than 0° and less than 90°
• in the figure above, ∠bcd is an acute angle because it measures 14°
• write another example of an acute angle from the figure:
• right angle - angle that measures exactly 90°
• in the figure above, ∠ecb is a right angle because it measures 90°
• write another example of a right angle from the figure:
• obtuse angle - angle that measures more than 90° and less than 180°
• in the figure above, ∠acd is an obtuse angle because it measures 166°
• write another example of an obtuse angle from the figure:
• straight angle - angle that measures exactly 180°
• in the figure above, ∠fcd is a straight angle because it measures 90°
• write another example of a straight angle from the figure:

angle pairs
special angle pairs can help you identify geometric relationships. you can use these angle pairs to find angle measures.

• adjacent angles - share a common side and a common vertex
• in the figure above, ∠ecb and ∠bcd are adjacent angles
• write another example of adjacent angles from the figure:
• vertical angles - two angles whose sides are opposite rays (share a vertex and sides are made of intersecting lines)
• in the figure above, ∠fcb and ∠acb are vertical angles
• write another example of vertical angles from the figure:
• complementary angles - two angles whose measures have a sum (add up to) 90° (they do not have to be adjacent)
• in the figure above, ∠acf and ∠fce are complementary angles
• supplementary angles - two angles whose measures have a sum (add up to) 180° (they do not have to be adjacent)
• in the figure above, ∠ace and ∠ecb are supplementary angles
• write another example of supplementary angles from the figure:

Explanation:

Step1: Identify adjacent angles

Adjacent angles share a common side and vertex. In the figure, $\angle ECA$ and $\angle ACB$ are adjacent as they share side $CA$ and vertex $C$.

Step2: Identify vertical angles

Vertical angles have sides as opposite - rays and share a vertex. $\angle FCE$ and $\angle ACD$ are vertical angles as their sides are formed by intersecting lines and they share vertex $C$.

Step3: Identify supplementary angles

Supplementary angles add up to $180^{\circ}$. $\angle FCB$ and $\angle BCD$ are supplementary since $\angle FCD = 180^{\circ}$ and $\angle FCB+\angle BCD=\angle FCD$.

Answer:

Adjacent angles: $\angle ECA$ and $\angle ACB$
Vertical angles: $\angle FCE$ and $\angle ACD$
Supplementary angles: $\angle FCB$ and $\angle BCD$