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3 years ago

Kari drew two parallel lines PQ and RS intersected by a transversal KL, as shown below:

Mathematics

1 answer:

Archy [21]3 years ago

5 0

Answer: Same-Side Interior Angles Theorem

Step-by-step explanation:

Same-Side Interior Angles Theorem says that when two lines are parallel and a transversal intersects it , then the angles on the same interior side are supplementary.

We are given that Two parallel lines PQ and RS are drawn with KL as a transversal intersecting PQ at point M and RS at point N.

Angle QMN is shown congruent to angle LNS.

Also, angle QML and angle SNK are the angles lies on the same side of the transversal.

It means the measure of angle QML is supplementary to the measure of angle SNK [ By Same-Side Interior Angles Theorem ]

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Answer:

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Step-by-step explanation:

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Ans

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3 years ago

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Let
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Read 2 more answers

A rectangle and a square have the same area. a. The width of the rectangle is w inches. The length of the rectangle is 15 inches

harkovskaia [24]

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Answer:

a) w(4w-15)

b) w²

c) w(4w -15) = w²

d) w = 5

e) 5 by 5

Step-by-step explanation:

a) If w is the width, and the length is 15 less than 4 times the width, then the length is 4w-15. The area is the product of length and width.

A = w(4w -15)

b) If w is the side length, the area of the square is (also) the product of length and width:

A = w²

c) Equating the expressions for area, we have ...

w(4w -15) = w²

d) we can subtract the right side to get ...

4w² -15w -w² = 0

3w(w -5) = 0

This has solutions w=0 and w=5. Only the positive solution is sensible in this problem.

The side length of the square is 5 units.

e) The rectangle is 5 units wide, and 4(5)-15 = 5 units long.

The rectangle and square have the same width and the same area, so the rectangle must be a square.

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3 years ago

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I assume you're looking for the value of x?

Combine like terms: 8x+5x+2x-11+6=180 -> 15x-5=180

Add 5 to both sides: 15x=185

Divide both sides by 15: x=12 1/3

So x is 12 1/3 or 37/3

Hope this helped!

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