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vitfil [10]
3 years ago
14

I really need help asap!!

Mathematics
1 answer:
Firdavs [7]3 years ago
5 0

Given:

A figure of a parallelogram.

The vertex angles are (12b+8)^\circ,(5b+2)^\circ,2a^\circ.

To find:

The values of a and b.

Solution:

We know that the pairs of consecutive angles of a parallelogram are supplementary angles. It mean their sum is 180 degrees.

(12b+8)^\circ+(5b+2)^\circ=180^\circ       (Supplementary angles)

(17b+10)^\circ=180^\circ

17b+10=180

Subtract 10 from both sides.

17b=180-10

17b=170

Divide both sides by 17.

b=\dfrac{170}{17}

b=10

Now,

(5b+2)^\circ=(5(10)+2)^\circ

(5b+2)^\circ=(50+2)^\circ

(5b+2)^\circ=52^\circ

And,

(5b+2)^\circ+2a^\circ=180^\circ       (Supplementary angles)

52^\circ+2a^\circ=180^\circ

2a^\circ=180^\circ-52^\circ

2a^\circ=128^\circ

Divide both sides by 2.

a^\circ=\dfrac{128^\circ}{2}

a^\circ=64^\circ

a=64

Therefore, the value of a is 64 and the value of b is 10.

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Solve the right triangle​ ABC, with Cequals90degrees. Aequals58.3degrees​, cequals24.8 ft
horsena [70]

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Step-by-step explanation:

If ABC is a right triangle, where the right angle is B, then

  • The hypotenuse of the triangle is b and a , c are its legs
  • sin(A) = \frac{a}{b}
  • sin(C) = \frac{c}{b}
  • b=\sqrt{a^{2}+c^{2}}
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∵ ABC is a right triangle

∵ m∠C = 90°

∴ c is the hypotenuse and a , b are its legs

∵ m∠A = 58.3°

- The sum of the two acute angles in the right triangle = 90°

∴ m∠A + m∠B = 90°

- Substitute the measure of angle A

∴ 58.3 + m∠B = 90

- Subtract 58.3 from both sides

∴ m∠B = 31.7°

∵ sin(A) = \frac{a}{c}

∵ c = 24.8 feet

∴ sin(58.3) = \frac{a}{24.8}

- By using cross multiplication

∴ a = (24.8) × sin(58.3)

∴ a = 21.1 ft

∵ sin(B) = \frac{b}{c}

∵ c = 24.8 feet

∴ sin(31.7) = \frac{b}{24.8}

- By using cross multiplication

∴ b = (24.8) × sin(31.7)

∴ b = 13.0 ft

m∠B = 31.7° , a = 21.1 ft , b = 13.0 ft

Learn more:

You can learn more about solving the triangle in brainly.com/question/12985572

#LearnwithBrainly

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