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mafiozo [28]
3 years ago
7

What is the measure of XYZ?

Mathematics
2 answers:
Anuta_ua [19.1K]3 years ago
8 0

<XYZ = 1/2(86 + 44)

<XYZ = 1/2 (130)

<XYZ = 65


Answer

B. 65

kirza4 [7]3 years ago
7 0

Answer:

Option B. 65°

Step-by-step explanation:

By the theorem of intersecting chords of a circle.

∠ XYZ = \frac{1}{2} [m(arc VM) + m(arc XZ)]

Now by putting values of arc VM and arc XZ,  we can get the measure of

∠ XYZ.

∠ XYZ = \frac{1}{2} [44 + 86]

           = \frac{1}{2} (130)

           = 65°

Therefore, The measure of XYZ = 65°, Option B.

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.
Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

Hypotenuse:37.56

Other\ Legs: 26.56

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

y = 11 + x

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

y^2 = x^2 + x^2

y^2 = 2x^2

This gives:

(11+x)^2 = 2x^2

Open bracket

121 + 22x + x^2= 2x^2

Collect like terms

2x^2 - x^2 -22x - 121 = 0

x^2 -22x - 121 = 0

Using quadratic formula:

x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}

x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}

x = \frac{-(-22)\±\sqrt{968}}{2*1}

x = \frac{22\±31.11}{2}

Split

x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\

x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}

x can not be negative.

So:

x = \frac{53.11}{2}

x = 26.56

Recall that:

y = 11 + x

y = 11 + 26.56

y = 37.56

Hence, the dimensions are:

Hypotenuse:37.56

Other\ Legs: 26.56

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Answer:

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Step-by-step explanation:

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Complete Question

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