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pentagon [3]
3 years ago
9

Use the exterior angle theorem to find the value of x in the triangle below.

Mathematics
1 answer:
Arisa [49]3 years ago
7 0

Answer:

Option A

Step-by-step explanation:

By using the definition of an exterior angle of a triangle,

"Measure of the exterior angle of a triangle is equal to the sum of measures of the opposite interior angles"

m∠STP = m∠SWT + m∠STW

Substitute the measures of the angles from the picture attached,

15x = (7x + 1) + (7x + 6)

15x = (7x + 7x) + (1 + 6)

15x = 14x + 7

15x - 14x = 7

x = 7

Therefore, Option A will be the correct option.

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In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?
vichka [17]

Answer:

x = 5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}

Step-by-step explanation:

We need to solve the quadratic equation

6 = x^2 -10x

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Using quadratic formula to solve the quadratic equation

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

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Putting values in the quadratic formula

x=\frac{-(-10)\pm\sqrt{(-10)^2-4(1)(-6)}}{2(1)}\\x=\frac{10\pm\sqrt{100+24}}{2}\\x=\frac{10\pm\sqrt{124}}{2}\\x=\frac{10\pm\sqrt{2*2*31}}{2}\\x=\frac{10\pm\sqrt{2^2*31}}{2}\\x=\frac{10\pm2\sqrt{31}}{2}\\x = 5\pm\sqrt{31}

So, x=5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}

3 0
3 years ago
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Answer:

PQ = 4

Step-by-step explanation:

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SO ; PQ = 4 , QR = 4

I hope I helped you^_^

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3 years ago
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