I need help on answering this question

Mathematics

1 answer:

liubo4ka [24]4 years ago

7 0

Answer:

<h2>The answer is 72°</h2>

Step-by-step explanation:

Since < RQS = < QLK and < RQS = x

< QLK is also x

< QLK and < KLM lie on a straight line

Angles on a straight line add up to 180°

To find x add < QLK and < KLM and equate them to 180°

That's

< QLK + < KLM = 180°

x + x - 36 = 180

2x = 180 - 36

2x = 144

Divide both sides by 2

We have the final answer as

Hope this helps you

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The plane is tiled by congruent squares of side length $a$ and congruent pentagons of side lengths $a$ and $\frac{a\sqrt{2}}{2}$

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The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.

<h3>How to determine the percentage?</h3>

Since the side of the small square is a, then the area of the tile is

given by:

Area of tiles = 9a²

<u>Note:</u> With an area of 9a², 4a² is covered by squares while 5a² by pentagons.

This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:

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Read more on area of square here: brainly.com/question/8902873

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Complete Question:

The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58