Given that ∠AXB is complementary to both ∠CYD and ∠FZE, and m∠AXB=20∘, what is m∠CYD+m∠FZE?
Complementary angles
A. 70∘
B. 110∘
C. 140∘
D. 160∘
Since ∠AXB is complementary to both ∠CYD and ∠FZE, we know that:
m∠AXB + m∠CYD = 90°
m∠AXB + m∠FZE = 90°
We also know that m∠AXB = 20°.
Substituting this value into the equations above, we get:
20° + m∠CYD = 90°
20° + m∠FZE = 90°
Solving for each unknown angle, we get:
m∠CYD = 70°
m∠FZE = 70°
Therefore,
m∠CYD + m∠FZE = 70° + 70° = 140°
The answer is (C) 140°.
To solve this problem, we need to use the fact that complementary angles add up to 90 degrees.
Given that ∠AXB is complementary to both ∠CYD and ∠FZE, we know that:
m∠AXB + m∠CYD = 90 degrees (equation 1)
m∠AXB + m∠FZE = 90 degrees (equation 2)
We are also given that m∠AXB = 20 degrees.
Substituting this value into equations 1 and 2, we get:
20 + m∠CYD = 90 (equation 3)
20 + m∠FZE = 90 (equation 4)
Solving equation 3 for m∠CYD, we subtract 20 from both sides:
m∠CYD = 90 - 20
m∠CYD = 70 degrees
Solving equation 4 for m∠FZE, we also subtract 20 from both sides:
m∠FZE = 90 - 20
m∠FZE = 70 degrees
Now, we can find the sum of m∠CYD and m∠FZE:
m∠CYD + m∠FZE = 70 + 70
m∠CYD + m∠FZE = 140 degrees
Therefore, the answer is C. 140 degrees.