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Alexeev081 [22]
3 years ago
8

Find m Give explanation please

Mathematics
1 answer:
Crazy boy [7]3 years ago
5 0

Answer:

m < FGN = 88°

Step-by-step explanation:

The exterior angle theorem states that the measure of each <em>exterior</em> angle of a triangle is equal to the <u>sum</u> of the <em>opposite</em> and non-adjacent interior angles (also known as <u>remote interior angles</u>).

Given the exterior angle, m <FGN = (7x + 18)°, and the two remote interior angles, m < E = 38° and m < F = (6x - 10)°:

The following equality statement can be established according to the exterior angle theorem:

m < E  + m < F  = m <FGN

38 + 6x - 10 = 7x + 18

Combine like terms:

28 + 6x = 7x + 18

Subtract 6x from both sides:

28 + 6x - 6x = 7x - 6x + 18

28 = x + 18

Subtract 18 from both sides:

28 - 18 = x + 18 - 18

10 = x

Next, substitute the value of x = 10 into the equality statement to determine whether it is the correct value of x, and to find the measures of < FGE and < F.

m < E  + m < F  = m <FGN

38° + (6x - 10)° = (7x + 18)°

38 + 6(10) - 10 = 7(10) + 18

38 + 60 - 10 = 70 + 18

88 = 88 (True statement).

Therefore, m < FGN = 88°

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The best way to do this is to draw a picture of ΔFKL and include line segment KM that is perpendicular to FL.  This creates ΔFKM which is a 45°-45°-90° triangle and ΔLKM which is a 30°-60°-90° triangle.

Find the lengths of FM and ML.  Then, FM + ML = FL

<u>FM</u>

ΔFKM (45°-45°-90°): FK is the hypotenuse so FM = \frac{a}{\sqrt{2}} = \frac{a\sqrt{2} }{2}

<u>ML</u>

ΔLKM (30°-60°-90°): from ΔFKM, we know that KM = \frac{a\sqrt{2} }{2} , so KL = \frac{a}{\sqrt{6}} = \frac{a\sqrt{6} }{6}  

<u>FM + ML = FL</u>

(\frac{3}{3})\frac{a\sqrt{2}  }{2} + \frac{a\sqrt{6}  }{6}

= \frac{3a\sqrt{2} + a\sqrt{6} }{6}

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3 years ago
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What are the first two answers? #16 and #17
Luden [163]
Answer to number 16 is 27 and 17 is 2
5 0
3 years ago
Please help me I will really appreciate it!!!
Margarita [4]
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4 0
2 years ago
I NEED HELP W THIS QUESTION!!
Kobotan [32]

Answer:

A

Step-by-step explanation:

To find the value you can just find 12% of each number (trial and error), until one of them gives you 90 as an answer:

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C) 360

360 * 0.12 = 43.2

D) 1168

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I hope this helps!

8 0
3 years ago
Zamir needs to determine the height of the building
Svetach [21]

Answer:

Height of the building = 115.4 ft.

Step-by-step explanation:

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By applying Pythagoras theorem in ΔABP,

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By applying sine rule in ΔCDE,

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CD = CE × \frac{1}{2}

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3 years ago
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