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maks197457 [2]
3 years ago
13

What value of x will make the question below truw?

Mathematics
1 answer:
MatroZZZ [7]3 years ago
7 0
1/2 (6x - 10) + 10 = 5x - 13

(6x/2) - (10/2) + 10 = 5x - 13

3x - 5 + 10 = 5x - 13

3x - 5x = -13 + 5 - 10

-2x = -18

x = -18 / -2

x = 9

D.) x = 9

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Answer:

m < A = 60º

m < B = 30º

Step-by-step explanation:

The given sides on this triangle are: 6, 6\sqrt{3}, and 12

Any triangle with the angles of 30º - 60º - 90º always has side lengths in this proportion:

x, x\sqrt{3}, 2x

We can line this up with the given sides. If x is 6, then 2x would be 12.

x : x\sqrt{3} : 2x = 6 : 6\sqrt{3} : 12

Angle B is across from 6, the shortest side. That also means that it corresponds to x, or the smallest angle in the proportion, 30º.

m < B = 30º

Solving for < A:

Method 1) Sum of Angles in a Triangle

Since we already know that one angle is right and therefore 90º and m < B is 30º, we can subtract these from the total sum of angle measures in a triangle to get the last angle, < A.

180º - 90º - 30º = 60º

m < A = 60º

Method 2) Using the second part of the proportion

Since m < A is across from the second largest side, we know that it is equal to x\sqrt{3} (6\sqrt{3} in this question) or 60º in the angle proportion.

This means that m < A = 60º

Let me know if you have any questions!

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