Question

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: ∠eca and
• 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: ∠fce and
• 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: ∠f

Explanation:

Step1: Identify acute - angle

Look for angles between 0° and 90°. $\angle ECD$ could be another acute - angle if its measure is in the right range.

Step2: Identify right - angle

Find angles equal to 90°. $\angle FCE$ could be another right - angle if it measures 90°.

Step3: Identify obtuse - angle

Search for angles between 90° and 180°. $\angle FCA$ could be another obtuse - angle if its measure is in this range.

Step4: Identify straight - angle

Look for angles equal to 180°. There may not be another obvious straight - angle shown if the figure is as presented.

Step5: Identify adjacent angles

Find pairs sharing a common side and vertex. $\angle FCD$ and $\angle DCB$ are adjacent angles.

Step6: Identify vertical angles

Find pairs with opposite - ray sides. $\angle ACD$ and $\angle FCB$ are vertical angles.

Step7: Identify complementary angles

Find pairs summing to 90°. $\angle BCD$ and $\angle DCE$ could be complementary if their sum is 90°.

Step8: Identify supplementary angles

Find pairs summing to 180°. $\angle ACB$ and $\angle BCF$ are supplementary if their sum is 180°.

Answer:

Acute angle: $\angle ECD$ (if measure is between 0° and 90°)
Right angle: $\angle FCE$ (if measure is 90°)
Obtuse angle: $\angle FCA$ (if measure is between 90° and 180°)
Straight angle: None obvious
Adjacent angles: $\angle FCD$ and $\angle DCB$
Vertical angles: $\angle ACD$ and $\angle FCB$
Complementary angles: $\angle BCD$ and $\angle DCE$ (if sum is 90°)
Supplementary angles: $\angle ACB$ and $\angle BCF$ (if sum is 180°)