Question

complementary, supplementary, linear pair
show all work!
find the measure of angle b.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Identify geometric relationships

Using the Complementary Angles and Linear Pair Postulate knowledge points

• Questions 1, 2, 3, 5, 7, and 8 show a right-angle symbol (\(90^\circ\)) indicating that the two adjacent angles are complementary.
• Questions 4 and 6 show angles on a straight line or forming a linear pair, meaning they are supplementary (\(180^\circ\)).

Solve complementary angle problems

Using the Complementary Angles knowledge point

• Question 1: \(59^\circ + b = 90^\circ \implies b = 31^\circ\)
• Question 2: \(64^\circ + b = 90^\circ \implies b = 26^\circ\)
• Question 3: \(36^\circ + b = 90^\circ \implies b = 54^\circ\)
• Question 5: \(b + 32^\circ = 90^\circ \implies b = 58^\circ\)
• Question 7: \(b + 58^\circ = 90^\circ \implies b = 32^\circ\)
• Question 8: \(b + 57^\circ = 90^\circ \implies b = 33^\circ\)

Solve supplementary angle problems

Using the Linear Pair Postulate knowledge point

• Question 4: \(76^\circ + b = 180^\circ \implies b = 104^\circ\)
• Question 6: \(b + 43^\circ = 180^\circ \implies b = 137^\circ\)

Answer:

No.	Answer
2	\(b = 26^\circ\)
3	\(b = 54^\circ\)
4	\(b = 104^\circ\)
5	\(b = 58^\circ\)
6	\(b = 137^\circ\)
7	\(b = 32^\circ\)
8	\(b = 33^\circ\)