Solve for X

Mathematics

1 answer:

Phantasy [73]2 years ago

4 0

Answer:

x = 48

Step-by-step explanation:

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

156° is an exterior angle of the triangle, then

108 + x = 156 ( subtract 108 from both sides )

x = 48

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$\text{Let the side of square 1, square 2 and square 3 be x, y and z respectively.}\\\\\text{Given that,}\\\\\text{Perimeter of square 1,~~ p =100 units.}\\\\\text{So}~ x=\dfrac p 4 = \dfrac{100}4 =25~\text{units.}\\\\\\\text{Area of square 2, a = 225 units}^2\\\\\text{So}~y = \sqrt{a} = \sqrt {225} = 15~ \text{units.}\\\\\text{Use Pythagorean theorem to find z}^2\\\\x^2 =y^2 +z^2 \\\\\implies 25^2 = 15^2 +z^2\\\\\implies z^2 = 625 - 225 = 400\\\\\\$