Chapter Test
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Supplementary angles add up to 180^(∘) and complementary angles add up to 90^(∘).
Supplementary Angles: ∠ AFB and ∠ BFE, ∠ AFC and ∠ EFC, ∠ AFD and ∠ DFE
Complementary Angles: ∠ AFB and ∠ BFC, ∠ CFD and ∠ DFE
m∠ DFE = 63^(∘)
m∠ BFC = 51 ^(∘)
m∠ BFE = 141 ^(∘)
Let's think about each of the given tasks one at a time, starting with finding all of the supplementary angles.
Supplementary angles are any two angles whose sum is 180^(∘). Since ∠ AFE is 180^(∘), any division of it will create supplementary angles. Using FB as the divider, we get the following scenario.
This means that ∠ AFB and ∠ BFE are supplementary angles. We can also use FC as a divider.
This means that ∠ AFC and ∠ EFC are also supplementary angles. Finally, we can divide ∠ AFE using FD.
Therefore, ∠ AFD and ∠ DFE is our last pair of supplementary angles.
Complementary angles are any two angles whose sum is 90^(∘). Since ∠ AFE is a straight angle and ∠ CFE is a right angle, ∠ AFC is also a right angle measuring 90^(∘).
Any division of either of these will create complementary angles.
Looking at the left-hand side, we can see that ∠ AFB and ∠ BFC are complementary angles. Similarly, on the right-hand side, ∠ CFD and ∠ DFE are also complementary angles.
From the diagram, we know that m∠ CFD is 27^(∘).
m∠ CFD= 27^(∘)
LHS-27^(∘)=RHS-27^(∘)
We are given that m∠ AFB is 39^(∘).
m∠ AFB= 39^(∘)
LHS-39^(∘)=RHS-39^(∘)
Finally, we know that ∠ AFB and ∠ BFE are supplementary angles.
m∠ AFB= 39^(∘)
LHS-39^(∘)=RHS-39^(∘)