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Veseljchak [2.6K]
2 years ago
6

What is the value of xfind the value of f​

Mathematics
2 answers:
zvonat [6]2 years ago
6 0

Answer:

x = 20 , f = 40

Step-by-step explanation:

4x and 5x are a linear pair and sum to 180° , then

4x + 5x = 180

9x = 180 ( divide both sides by 9 )

x = 20

then

5x = 5 × 20 = 100° and 3x = 3 × 20 = 60°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

5x is an exterior angle of the triangle , then

f + 3x = 5x , that is

f + 60 = 100 ( subtract 60 from both sides )

f = 40

Black_prince [1.1K]2 years ago
4 0

Answer:

x = 20°

f = 40°

Step-by-step explanation:

4x + 5x = 180°

because a straight line is 180°

so 9x = 180°

1x = 180 ÷ 9

1x = 20

all angles in a triangle add together is 180°

so 7x + f = 180°

1x = 20

7x = 20 × 7

7x = 140°

f = 180° - 140 °

f = 40°

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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
Musya8 [376]
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
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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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So, we have two equations on x, y and z:

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Substitute 2x + y by 36 from (eq.1) in (eq.2):

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And solve for z:

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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Answer:

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Step-by-step explanation:

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