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SOLVE EQUATIONS WITH COMPLEMENTARY ANGLES

PRACTICE:
1. 2x-4, 90
2. 4x-2, 90
3. 7x-9, 90
4. 15, 60, 30
5. 57, 54

QUICK CHECK:
1. (7x+1)°=90°
2. (7x−22)°=90°
3. 13
4. 33° and 57°
5. 6

yw!! make sure to eat well and stay hydrated!! good luck <3

1 answer

Sure! Let's solve the equations involving complementary angles. Complementary angles are two angles that add up to 90 degrees.

PRACTICE:

  1. 2x - 4, 90

    • Let \( y = 2x - 4 \).
    • \( y + 90 = 90 \)
    • So, \( 2x - 4 + 90 = 90 \)
    • \( 2x - 4 = 0 \)
    • \( 2x = 4 \)
    • \( x = 2 \)

  2. 4x - 2, 90

    • Let \( y = 4x - 2 \).
    • \( y + 90 = 90 \)
    • So, \( 4x - 2 + 90 = 90 \)
    • \( 4x - 2 = 0 \)
    • \( 4x = 2 \)
    • \( x = 0.5 \)

  3. 7x - 9, 90

    • Let \( y = 7x - 9 \).
    • \( y + 90 = 90 \)
    • So, \( 7x - 9 + 90 = 90 \)
    • \( 7x - 9 = 0 \)
    • \( 7x = 9 \)
    • \( x = \frac{9}{7} \approx 1.29 \)

  4. 15, 60, 30

    • We need to check if these angles are complementary pairs. However, this is more straightforward since they're just listed:
    • \( 15 + 75 = 90 \) (not mentioned but implied)
    • Angles: \( 15°, 30°, and 60° \) are not a pair of complementary angles since \( 15 + 30 + 60 = 105 \), requires more context on what is intended here.

  5. 57, 54

    • We check if angles are complementary:
    • \( 57 + 54 = 111 \) (not complementary)

QUICK CHECK:

  1. (7x + 1)° = 90°

    • \( 7x + 1 = 90 \)
    • \( 7x = 89 \)
    • \( x = \frac{89}{7} \approx 12.71 \)

  2. (7x - 22)° = 90°

    • \( 7x - 22 = 90 \)
    • \( 7x = 112 \)
    • \( x = \frac{112}{7} = 16 \)

  3. 13 (this seems like a standalone answer, not an equation)

  4. 33° and 57°:

    • Check if they are complementary: \( 33 + 57 = 90 \) (complementary)

  5. 6 (again, similar to before, this seems like a standalone answer)

Make sure to check each step and match the equations or context for each pair of angles you want to analyze more.

And thank you for your kind reminder! Stay healthy and hydrated! 🌟