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chubhunter [2.5K]
2 years ago
11

Angle A and angle B are complementary angles. If m∡a = 4x and m∡b = 3x +13, what is the measure of the smaller angle?

Mathematics
1 answer:
bagirrra123 [75]2 years ago
5 0

Answer:

Step-by-step explanation:

Complementary angles mean two two angles sum with equal 90 degrees. Therefore you would need to create an equation to solve for the value of x.

4x+3x+13=90

-13 -13

7x=77

/7 /7

X=11

Now plug in the value of x.

A=4(11) B=3(11)+13

A=44. B=33+13

B=46

Angle a is the smaller angle and measures at 44°

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In triangle KLM, if K is congruent to L, KL = 9x - 40, LM = 7x - 37, & KM = 3x + 23, find x & the measure of each angle.
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Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°

<u>Step-by-step explanation:</u>

Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL

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3x + 23 = 7x - 37

       23 = 4x - 37

       60 = 4x

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    = 95

Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.

  • Since N is the midpoint of KL and KL = 95, then NL = 47.5
  • Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse

Use trig to solve for ∠L (which equals ∠K):

cos ∠L = \frac{adjacent}{hypotenuse}

cos ∠L = \frac{47.5}{68}

      ∠L = cos⁻¹ (\frac{47.5}{68})

      ∠L = 45.7  

Triangle sum Theorem:

∠K + ∠L + ∠M = 180°    

45.7 + 45.7 + ∠M = 180

       91.4     + ∠M = 180

                      ∠M = 88.6

       

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