Question

1. (m\angle deb = \underline{\qquad\qquad})
2. (m\angle abd = \underline{\qquad\qquad})
3. (m\angle abd = \underline{\qquad\qquad})
4. if (\angle abd) and (\angle dbc) are complementary where (\angle abd = (2x + 22)^\circ) and (\angle dbc = (6x - 4)^\circ). what is (m\angle dbc)?
5. if (\angle abd) and (\angle dbc) form a linear pair where (\angle abd = (2x + 68)^\circ) and (\angle dbc = (12x + 28)^\circ). what is (m\angle abd)?
6. if (\angle aeb) and (\angle dec) are vertical angles where (\angle aeb = (8x - 9)^\circ) and (\angle dec = (3x + 31)^\circ). what is (m\angle aeb)?
7. if (\angle aeb) and (\angle dec) are vertical angles where (\angle aeb = (10x + 12)^\circ) and (\angle dec = (13x - 9)^\circ). what is (m\angle dec)?
8. if (\angle abd) and (\angle dbc) are complementary where (\angle abd = (2x - 16)^\circ) and (\angle dbc = (8x + 6)^\circ). what is (m\angle abd)?
9. if (\angle abd) and (\angle dbc) form a linear pair where (\angle abd = (2x + 40)^\circ) and (\angle dbc = (8x + 20)^\circ). what is (m\angle dbc)?

Explanation:

Solve Question 7

Using the Vertical Angles Theorem knowledge point

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Solve Question 8

Using the Complementary Angles and Angle Addition Postulate knowledge points

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Solve Question 9

Using the Linear Pair Postulate knowledge point

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Solve Question 10

Using the Complementary Angles knowledge point

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Solve Question 11

Using the Linear Pair Postulate knowledge point

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Solve Question 12

Using the Vertical Angles Theorem knowledge point

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Solve Question 13

Using the Vertical Angles Theorem knowledge point

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Solve Question 14

Using the Complementary Angles knowledge point

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Solve Question 15

Using the Linear Pair Postulate knowledge point

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Answer:

Question 7

\(m\angle CEB = 22^\circ\) (Letter S)

Question 8

\(m\angle ABD = 34^\circ\) (Letter C)

Question 9

\(m\angle ABD = 86^\circ\) (Letter W)

Question 10

\(m\angle DBC = 50^\circ\) (Letter !)

Question 11

\(m\angle ABD = 80^\circ\) (Letter A)

Question 12

\(m\angle AEB = 55^\circ\) (Letter E)

Question 13

\(m\angle DEC = 82^\circ\) (Letter H)

Question 14

\(m\angle ABD = 4^\circ\) (Letter N)

Question 15

\(m\angle DBC = 116^\circ\) (Letter O)