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2 years ago

Find the m ∠YXZ. Show your Work

Mathematics

1 answer:

Charra [1.4K]2 years ago

6 0

Answer:

∠YXZ = 62°

Step-by-step explanation:

A straight line measures 180 degrees

The angle "8x - 14" PLUS its adjacent angle Z sum up to 180, so we can write:

Z + 8x - 14 = 180

Z = 180 +14 - 8x

Z = 194 - 8x

Sum of 3 angles of a triangle is 180 degrees, thus we can write:

X + Y + Z = 180

3x + 5 + 4x + 194 - 8x = 180

Now, we solve for x:

$3x + 5 + 4x + 194 - 8x = 180\\-x+199=180\\x = 199-180\\x=19$

The measure of ∠YXZ is "3x + 5", we substitute the value of x and find this angle to be:

3x + 5

3(19) + 5

Thus,

∠YXZ = 62°

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$A(B-C) = 4 \times (5-6) = 4 \times -1 = -4$

Let A = 4, B = 6 and C = 5

$A(B-C) = 4 \times (6-5) = 4 \times 1 = 4$

Let A = 5, B =4 and C = 6

$A(B-C) = 5 \times (4-6) = 5 \times -2 = -10$

Let A = 5, B = 6 and C = 4

$A(B-C) = 4 \times (6-4) = 4 \times 2 = 8$

Let A = 6, B = 4 and C = 5

$A(B-C) = 6 \times (4-5) = 6 \times -1 = -6$

Let A = 6, B = 5 and C = 4

$A(B-C) = 6 \times (6-5) = 6 \times 1 = 6$

Summarizing the above values in the form of a table:

$\begin{center}\begin{tabular}{ c c c c}A & B & C & A(B-C)\\ 4 & 5 & 6 & -4\\ 4 & 6 & 5 & 4\\ 5 & 4 & 6 & -10\\ 5 & 6 & 4 & 10\\ 6 & 4 & 5 & -6\\ 6 & 5 & 4 & 6\end{tabular}\end{center}$

So, the least possible result is -10.

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