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vodka [1.7K]
1 year ago
10

If AC is parallel to DE, find X

Mathematics
1 answer:
UNO [17]1 year ago
8 0

Answer: x = 50

Concept:

Here, we need to know the idea of alternative interior angles and the angle sum theorem.

<u>Alternative interior angles</u> are angles that are formed inside the two parallel lines, and the values are equal.

The <u>angle sum theorem</u> implies that the sum of interior angles of a triangle is 180°

If you are still confused, please refer to the attachment below or let me know.

Step-by-step explanation:

<u>Given information:</u>

AC ║ DE

∠ABC = 85°

∠A = 135°

<u>Find the value of ∠BAC</u>

∠A + ∠BAC = 180° (Supplementary angle)

(135°) + ∠BAC = 180°

∠BAC = 45°

<u>Find the value of ∠BCA</u>

∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)

(85°) + (45°) + ∠BCA = 180°

∠BCA = 50°

<u>Find the value of x (∠EBC)</u>

∠EBC ≅ ∠BCA (Alternative interior angles)

Since, ∠BCA = 50°

Therefore, ∠EBC = 50°

\Large\boxed{x=50}

Hope this helps!! :)

Please let me know if you have any questions

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Dmitry [639]

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d) Combine 2+3 to get 5. Combine 1+4 to get 5, which is 25. The answer is 5.

g) Combine 4+6 to get 10. Combine 70+-6 to get 64. Take the root of 64, leaving you with 10-8. Combine 10 + -8 to get 2. The answer is 2.

h) Combine 5+4 to get 9. Take the root of 36, leaving you with 18 + 6.  Combine 18 + 6 to get 24. The answer is 24.


5. [15 + 22 + 53] divided by [12 + 18] = [90] divided by [30] = 3 ribbons each.

6. (4 x 12) + (6 x 8) = 96 total.

4 0
3 years ago
_ 4. How many roots does the following equation have: 2x^4 – x^3 – 12x^2 – 25x + 5 = 0
vlada-n [284]

Answer:

B. 4

Step-by-step explanation:

The degree of the polynomial (the exponent of the highest term) is the total number of roots (including imaginary roots).

The degree of this polynomial is 4, so there are 4 roots.

7 0
3 years ago
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Nadusha1986 [10]

Answer:

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8 0
3 years ago
there is a beaker of 3.5% acid solution and a beaker of 6% acid solution in the science lab. Mr. Larson needs 200ml of 4.5% acid
disa [49]
Below are the choices:

A. 80 mL of the 3.5% solution and 120 mL of the 6% solution 

<span>B. 120 mL of the 3.5% solution and 80 mL of the 6% solution </span>

<span>C. 140 mL of the 3.5% solution and 60 mL of the 6% solution </span>

<span>D. 120 mL of the 3.5% solution and 80 mL of the 6% solution
</span>
Let fraction of 3.5% in final solution be p. 

<span>p * 3.5 + (1 - p) * 6 = 4.5 </span>

<span>3.5p + 6 - 6p = 4.5 </span>

<span>2.5p = 1.5 </span>

<span>p = 3/5 </span>

<span>3/5 * 200 = 120 </span>

<span>Therefore the answer is B. 120 ml of 3.5% and 80 ml of 6%.</span>

6 0
3 years ago
3. The number of children in 10 families of a locality are:
Anastaziya [24]

Answer:

Step-by-step explanation:

Mean = 2+4+3+4+2+0+3+5+1+6/ 10

= 30/10 = 3

6 0
3 years ago
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