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ivolga24 [154]
3 years ago
12

What is the value of x?

Mathematics
2 answers:
klio [65]3 years ago
8 0

Answer:

x = 84°

Step-by-step explanation:

The sum of the interior angles of a pentagon is equal to 540°.

x + 107 + 108 + 110 + 131 = 540

x + 456 = 540

x + 456 - 456 = 540 - 456

x = 84

alexgriva [62]3 years ago
4 0

Answer:

x = 84

Step-by-step explanation:

If you add up all of the internal angles in ANY pentagon it will be 540, so

x = 540 - (131+108+107+110)

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In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is
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Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
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The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

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(eq.1) 2x + y = 36
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36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12
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