Answer:
B) x = 13
Step-by-step explanation:
Complementary angles means that, when combined, they add up to 90°. In this case, the given Angles A & B are complementary, ∴
∠A + ∠B = 90°
It is given that:
m∠A = 23°
m∠B = (4x + 15)°
Plug in the corresponding terms to the corresponding variables:
m∠A + m∠B = 90°
(23)° + (4x + 15)° = 90°
First, combine like terms. Like terms are terms that share the same amount of the same variables:
4x + 15 + 23 = 90
4x + (15 + 23) = 90
4x + 38 = 90
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
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First, subtract 38 from both sides of the equation:
4x + 38 = 90
4x + 38 (-38) = 90 (-38)
4x = 90 - 38
4x = 52
Next, divide 4 from both sides of the equation:
(4x)/4 = (52)/4
x = 52/4
x = 13.
B) x = 13 is your answer.
Check: Plug in 13 for x in the given angle measurements, and combine the angles to obtain the measurement 90° (complementary):
m∠B = (4x + 15)
m∠B = (4 * 13) + 15
m∠B = 52 + 15
m∠B = 67°
m∠A + m∠B = 90°
m∠A + (67) = 90°
m∠A + 67 (-67) = 90 (-67)
m∠A = 90 - 67
m∠A = 23°
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Learn more about complementary angles, here:
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