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4 years ago

If m∠2 = 8x − 20, and m∠3 = 5x + 5, what is m∠2?

Mathematics

1 answer:

german4 years ago

4 0

Answer:

8x - 20

Step-by-step explanation:

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Quadrilateral ABCD is inscribed in a circle. m∠A is 64°, m∠B is (6x + 4)°, and m∠C is (9x − 1)°. What is m∠D?

Flauer [41]

Answer:

The m∠D is 98° ⇒ answer D

Step-by-step explanation:

* Lets revise some facts in the circle

- The quadrilateral is inscribed in a circle if its four vertices lie on the

circumference of the circle

- It is called a cyclic quadrilateral

- Every two opposite angles in it are supplementary means the

sum of their measures is 180°

∵ ABCD is inscribed in a circle

∴ ABCD is a cyclic quadrilateral

∵ ∠A and ∠C are opposite angles in the cyclic quadrilateral ABCD

∴ ∠A and ∠C are supplementary

∴ m∠A + m∠C = 180°

∵ m∠A = 64°

∵ m∠C = (9x - 1)°

∴ 64 + (9x - 1) = 180 ⇒ simplify

∴ 63 + 9x = 180 ⇒ subtract 63 from both sides

∴ 9x = 117 ⇒ divide both sides by 9

∴ x = 13

- Lets find the measure of ∠B

∵ m∠B = (6x + 4)°

∵ x = 13

∴ m∠B = 6(13) + 4 = 78 + 4 = 82°

- Lets find the measure of ∠D

∵ ∠B and ∠D are opposite angles in the cyclic quadrilateral ABCD

∴ ∠B and ∠D are supplementary

∴ m∠B + m∠D = 180°

∵ m∠B = 82°

∴ 82° + m∠D = 180° ⇒ subtract 82° from both sides

∴ m∠D = 98°

* The m∠D is 98°

3 0

4 years ago

What is the quotient of 0.3 and 0.6

Nikitich [7]

Answer:

0.5

Step-by-step explanation:

a quotient of something is basically dividing 1 number by another, 0.3/0.6 = 0.5

8 0

4 years ago

Read 2 more answers

What are the positive factors of 72

stich3 [128]

Answer: 1,2,3,4,6,8,9,12,18,24,36,72

4 0

4 years ago

Read 2 more answers

Which expression has the fewest number of significant figures

Brums [2.3K]

Answer:

18.3

18.3 only has three significant figures while the other numbers have more

5 0

3 years ago

Read 2 more answers

a_sh-v [17]

Answer:

40 children went on the cruise.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the number of adults on the cruise

y is the number of children on the cruise.

57 tickets were sold:

This means that $x + y = 57$ , and since we want the number of children y, $x = 57 - y$

Each adult had to pay $22 for the cruise and each child had to pay $10. The company's total receipts were $774.

This means that:

$22x + 10y = 774$

Since $x = 57 - y$

$22(57 - y) + 10y = 774$

$1254 - 22y + 10y = 774$

$12y = 480$

$y = \frac{480}{12}$

$y = 40$

40 children went on the cruise.

4 0

3 years ago