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Zorluk: KolayLines and Angles

Angles XX and YY are complementary angles. The measure of angle XX is (4x−10)∘(4x - 10)^\circ and the measure of angle YY is (x+20)∘(x + 20)^\circ. What is the measure of angle XX in degrees?

  1. 54Cevap
  2. B
    126
  3. C
    74
  4. D
    70

Cevap

54
Complementary angles have a sum of 90 degrees. By adding the expressions for angle X and angle Y together, we establish the equation (4x - 10) + (x + 20) = 90. Combining like terms yields 5x + 10 = 90. Subtracting 10 from both sides leaves 5x = 80, and dividing by 5 gives x = 16. The question asks for the measure of angle X, which is given by the expression (4x - 10). Substituting 16 for x gives 4(16) - 10 = 64 - 10 = 54 degrees.

Adım Adım Çözüm

1
Set up an equation based on the definition of complementary angles.
(4x−10)+(x+20)=90(4x - 10) + (x + 20) = 90
Complementary angles always sum to 90 degrees.
2
Combine like terms to simplify the equation.
5x+10=905x + 10 = 90
Grouping the x terms (4x + x = 5x) and constant terms (-10 + 20 = 10) simplifies the expression.
3
Solve for x by isolating the variable.
5x=80⇒x=165x = 80 \Rightarrow x = 16
Subtracting 10 from both sides and then dividing by 5 isolates x.
4
Substitute the value of x back into the original expression for angle X.
4(16)−10=64−10=544(16) - 10 = 64 - 10 = 54
The question asks for the specific measure of angle X, not just the algebraic value of x.

Anahtar Kavram

Complementary angles sum to 90 degrees, and unknown angle measures can be found by setting up and solving a linear equation.
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Lines and Angles

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